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R.S. Aggarwal solutions for Class 10 Mathematics chapter 10 - Quadratic Equations

Secondary School Mathematics for Class 10 (for 2019 Examination)

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R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

Secondary School Mathematics for Class 10 (for 2019 Examination) - Shaalaa.com

Chapter 10: Quadratic Equations

Chapter 10: Quadratic Equations solutions [Page 0]

Which of the following are quadratic equation in x? 

`x^2-x-3=0` 

Which of the following are quadratic equation in x? 

`2x^2+5/2xsqrt3=0`  

Which of the following are quadratic equation in x? 

`sqrt2x^2+7x+5sqrt2` 

Which of the following are quadratic equation in x? 

`1/3x^2+1/5x-2=0` 

 

Which of the following are quadratic equation in x? 

`x^2-3x-sqrtx+4=0`  

Which of the following are quadratic equation in x? 

`x-6/x=3` 

Which of the following are quadratic equation in x? 

`x^2-2/x=x^2` 

 

Which of the following are quadratic equation in x? 

`x^2-1/x^2=5` 

 

Which of the following are quadratic equation in x? 

`(x+2)^3=x^3-8` 

Which of the following are quadratic equation in x?  

(2x+3)(3x+2)=6(x-1)(x-2)

Which of the following are quadratic equation in x? 

`(x+1/x)^2=2(x+1/x)+3` 

Which of the following are the roots of` 3x^2+2x-1=0?` 

-1 

Which of the following are the roots of `3x^2+2x-1=0?` 

`1/3`

Which of the following are the roots of `3x^2+2x-1=0` 

`-1/2` 

 

Find the value of k for which x = 1is a root of the equation `x^2+kx+3=0` 

 

Find the value of a and b for which `x=3/4`and `x =-2` are the roots of the equation `ax^2+bx-6=0` 

 

`(2x-3) (3x+1)=0` 

 

 

`4x^2+5x=0`

`3x^2-243=0` 

 

`2x^2+x-6=0` 

 

`x^2+6x+5=0`  

 

 

`9x-3x-2=0` 

 

`x^2+12x+35=0` 

 

`x^2=18x-77` 

 

`6x^2+11x+3=0` 

 

`6x^2+x--12=0`

`3x^2x-1=0` 

`4x^2-9x=100`

`15x^2-28=x` 

 

`4-11x=3x^2` 

 

`48x^2-13x1=0` 

 

`x^2+2sqrt2x-6=0` 

 

`sqrt3x^2+10x7sqrt3=0` 

`sqrt3x^2+11x+6sqrt3=0` 

 

`3sqrt7x^2+4x-sqrt7=0` 

 

`sqrt7x^2-6x-13sqrt7=0` 

 

`4sqrt6x^2-13x-2sqrt6=0`  

`3x^2-2sqrt6x+2=0` 

 

`sqrt3x^2-2sqrt2x-2sqrt3=0` 

 

`x^2-(sqrt3+1)x+sqrt3=0` 

`x^2+3sqrt3-30=0` 

`sqrt2x^2+7x+5sqrt2=0` 

 

`5x^2+13x+8=0` 

 

`x^2-(1+sqrt2)x+sqrt2=0` 

 

`9x^2+6x+1=0`

`100x^2-20x+1=0` 

`2x^2-x+1/8=0` 

`10x1/x=3` 

 

`2/x^2-5/x+2=0` 

`2x^2+ax-a^2=0`

`4x^2+4bx-(a^2-b^2)=0` 

 

`4x^2-4a^2x+(a^4-b^4)=0` 

 

`x^2+5x-(a^2+a-6)=0` 

`x^2-2ax(4b^2-a^2)=0`  

 

`x^2-(2b-1)x+(b^2-b-20)=0` 

` x^2+6x-(a^2+2a-8)=0` 

`abx^2+(b^2-ac)x-bc=0` 

`x^2-4ax-b^2+4a^2=0` 

 

`4x^2-2(a^2+b^2)x+a^2b^2=0` 

 

`12abx^2-(9a^2-8b^2)x-6ab=0`

`a^2b^2x^2+b^2x-1=0` 

`9x^2-9(a+b)x+(2a^2+5ab+2b^2)=0`

`16/x-1=15/(x+1),x≠0,-1`

`4/x-3=5/(2x+3),x≠0,-3/2` 

 

`3/x+1-1/2=2/(3x-1),x≠-1,1/3` 

`1/x-1-1/(x+5)=6/7,x≠1,-5` 

`1/(2a+b+2x)=1/(2a)+1/b+1/(2x)`

`(x+3)/(x-2)-(1-x)/x=17/4` 

`3x-4/7+7/(3x-4)=5/2,x≠4/3` 

`x/(x-1)+x-1/4=4 1/4, x≠ 0,1` 

`x/(x+1)+(x+1)/x=2 4/15, x≠ 0,1` 

`(x-4)/(x-5)+(x-6)/(x-7)=31/3,x≠5,7` 

 

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3,x≠2,4` 

 

`1/(x-2)+2/(x-1)=6/x,≠0,1,2` 

`1/(x+1)+2/(x+2)=5/(x+4),x≠-1,-2,-4`

`3((3x-1)/(2x+3))-2((2x+3)/(3x-1))=5,x≠1/3,-3/2` 

`3((7x+1)/(5x-3))-4((5x-3)/(7x+1))=11,x≠3/5,-1/7` 

 

`((4x-3)/(2x+1))-10((2x+1)/(4x-3))=3,x≠-1/2,3/4` 

`(x/(x+1))^2-5(x/(x+1)+6=0,x≠b,a` 

`a/(x-b)+b/(x-a)=2,x≠b,a` 

`a/((ax-1))+b/((bx-1))=(a+b),x≠1/a,1/b` 

`3^((x+2))+3^(-x)=10`

`4^((x+1))+4^((1-x))=10`

`2^2x-3.2^((x+2))+32=0`

Chapter 10: Quadratic Equations solutions [Page 0]

`x^2-6x+3=0` 

`x^2-4x+1=0`

`x^2+8x-2=0`

`4x^2+4sqrt3x+3=0` 

`2x^2+5x-3=0`

`3x^2-x-2=0` 

`8x^2-14x-15=0`

`7x^2+3x-4=0` 

`3x^2-2x-1=0` 

`5x^2-6x-2=0` 

`2/x^2-5/x+2=0` 

 

`4x^2+4bx-(a^2-b^2)=0`

`x^2-(sqrt2+1)x+sqrt2=0` 

`sqrt2x^3-3x-2sqrt2=0`

`sqrt3x^2+10x+7sqrt3=0` 

By using the method of completing the square, show that the equation `2x^2+x+4=0` has no real roots.  

Chapter 10: Quadratic Equations solutions [Page 0]

` 2x^2-7x+6=0` 

`3x^2-2x+8=0` 

`2x^2-5sqrt2x+4=0` 

 

 

`sqrt3x^2+2sqrt2x-2sqrt3=0` 

`(x-1)(2x-1)=0`

`11-x=2x^2`

`x^2-4x-1=0` 

Find the roots of the each of the following equations, if they exist, by applying the quadratic formula: 

`x^2-4x-1=0`

`x^2-6x+4=0` 

 

`2x^2+x-4=0`

`25x^2+30x+7=0`

The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers. 

`16x^2+2ax+1`

`15x^2-28=x` 

 

`2x^2-2sqrt2x+1=0` 

`sqrt2x^2+7+5sqrt2=0`

`sqrt3x^2+10x-8sqrt3=0` 

`sqrt3x^2-2sqrt2x-2sqrt3=0` 

 

`2x^2+6sqrt3x-60=0` 

 

`4sqrt3x^2+5x-2sqrt3=0` 

`3x^2-2sqrt6x+2=0`

`2sqrt3x^2-5x+sqrt3=0`

`x^2+x+2=0` 

 

`2x^2+ax-a^2=0`

`x^2-(sqrt3+1)x+sqrt3=0` 

 

`2x^2+5sqrt3x+6=0` 

`3x^2-2x+2=0.b`

`x+1/x=3,x≠0` 

`1/x-1/(x-2)=3,x≠0,2` 

`x-1/x=3,x≠0` 

`3/n x^2 n/m=1-2x` 

 

`36x^2-12ax+(a^2-b^2)=0` 

`x^2-2ax+(a^2-b^2)=0` 

`x^2-2ax-(4b^2-a^2)=0`

`x^2+6x-(a^2+2a-8)=0` 

`x^2+5x-(a^+a-6)=0` 

 

`x^2-4ax-b^2+4a^2=0` 

 

`4x^2-4a^2x+(a^4-b^4)=0` 

 

`4x^2-4bx-(a^2-b^2)=0` 

 

`x^2-(2b-1)x+(b^2-b-20)=0`

`3a^2x^2+8abx+4b^2=0`

`a^2b^2x^2-(4b^4-3a^4)x-12a^2b^2=0,a≠0  and b≠ 0` 

 

`12abx^2-(9a^2-8b^2)x-6ab=0,` `Where  a≠0 and b≠0`                                                                                                                     

Chapter 10: Quadratic Equations solutions [Page 0]

Find the nature of roots of the following quadratic equations: 

`2x^2-8x+5=0` 

 

Find the nature of roots of the following quadratic equations: 

` 3x^2-2sqrt6x+2=0` 

Find the nature of roots of the following quadratic equations: 

`5x^2-4x+1=0`

`5x^2-4x+1=0` 

Find the nature of roots of the following quadratic equations: 

`12x^2-4sqrt15x+5=0` 

Find the nature of roots of the following quadratic equations: 

`x^2-x+2=0`

If a and b are distinct real numbers, show that the quadratic equations 

`2(a^2+b^2)x^2+2(a+b)x+1=0` has no real roots. 

Show that the roots of the equation `x^2+px-q^2=0` are real for all real values of p and q.

For what values of k are the roots of the quadratic equation `3x^2+2kx+27` real and equal ?  

 

For what value of k are the roots of the quadratic equation `kx(x-2sqrt5)+10=0`real and equal. 

For what values of p are the roots of the equation `4x^2+px+3=0` real and equal? 

Find the nonzero value of k for which the roots of the quadratic equation `9x^2-3kx+k=0` are real and equal. 

Find the values of k for which the quadratic equation `(3k+1)x^2+2(k+1)x+1=0`  has real and equal roots.  

Find the value of p for which the quadratic equation `(2p+1)x^2-(7p+2)x+(7p-3)=0` has real and equal roots. 

Find the values of p for which the quadratic equation `(p+1)x^2-6(p+1)x+3(p+9)=0` `p≠-11`has equal roots. Hence find the roots of the equation.

 

If -5 is a root of the quadratic equation `2x^2+px-15=0` and the quadratic equation `p(x^2+x)+k=0` 0has equal roots, find the value of k. 

If 3 is a root of the quadratic equation` x^2-x+k=0`  find the value of p so that the roots of  the equation  `x^2+2kx+(k^2+2k+p)=0` are equal. 

 

If -4 is a root of the equation `x^2+2x+4p=0` find the value of k for the which the quadratic  equation ` x^2+px(1+3k)+7(3+2k)=0` has equal roots. 

If the quadratic equation `(1+m^2)x^2+2mcx+(c^2-a^2)=0` has equal roots, prove that  `c^2=a^2(1+m^2)`  

If the roots of the quadratic equation `(c^2-ab)x^2-2(a^2-bc)x+(b^2-ac)=0` are real and equal, show that either  a=0  or  `(a^3+b^3+c^3=3abc)` 

 

Find the value of p for which the quadratic equation `2x^2+px+8=0` has real roots. 

Find the value of a for which the equation `(α-12)x^2+2(α-12)x+2=0` has equal roots.  

Find the value of k for which the roots of `9x^2+8kx+16=0` are real and equal 

 

Find the values of k for which the given quadratic equation has real and distinct roots:  

`kx^2+6x+1=0`

Find the values of k for which the given quadratic equation has real and distinct roots: 

`x^2-kx+9=0` 

Find the values of k for which the given quadratic equation has real and distinct roots: 

`9x^2+3kx+4=0` 

 

 

Find the values of k for which the given quadratic equation has real and distinct root:  

`5x^2-kx+1=0` 

 

 

If a and b are real and a ≠ b then show that the roots of the equation 

`(a-b)x^2+5(a+b)x-2(a-b)=0`are equal and unequal. 

If the roots of the equation `(a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0`are equal, prove that `a/b=c/d`

If the roots of the equations `ax^2+2bx+c=0` and `bx^2-2sqrtacx+b=0`are simultaneously real then prove that `b^2=ac`

Chapter 10: Quadratic Equations solutions [Page 0]

The sum of a natural number and its square is 156. Find the number. 

 

The sum of natural number and its positive square root is 132. Find the number. 

 

The sum of two natural number is 28 and their product is 192. Find the numbers. 

The sum of the squares of two consecutive positive integers is 365. Find the integers. 

 

The sum of the squares of two consecutive positive even numbers is 452. Find the numbers. 

 

The product of two consecutive positive integers is 306. Find the integers.

Two natural number differ by 3 and their product is 504. Find the numbers. 

Find two consecutive multiples of 3 whose product is 648.

Find the tow consecutive positive odd integer whose product s 483. 

Find the two consecutive positive even integers whose product is 288. 

The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers . 

 

The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.

The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers. 

 

The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers 

The sum of the squares two consecutive multiples of 7 is 1225. Find the multiples. 

The sum of natural number and its reciprocal is `65/8` Find the number 

Divide 57 into two parts whose product is 680. 

Divide 27 into two parts such that the sum of their reciprocal is `3/20` 

Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.

Divide two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.

The difference of the squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

Three consecutive positive integers are such that the sum of the square of the first and product of the other two is 46. Find the integers.

A two-digit number is 4 times the sum of its digits and twice the product of digits. Find the number. 

A two-digit number is such that the product of its digits is 14. If 45 is added to the number, the digit interchange their places. Find the number. 

 

The denominator of a fraction is 3 more than its numerator. The sum of the fraction and its reciprocal is `2 9/10` Find the fraction. 

The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by `1/15`
. Find the fraction

The sum of a number and its reciprocal is `2 1/30` Find the number. 

A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students. 

300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.

In a class test, the sum of Kamal’s marks in mathematics and English is 40. Had he got 3 marks more in mathematics and 4 marks less in English, the product of the marks would have been 360. Find his marks in two subjects separately.

Some students planned a picnic. The total budget for food was ₹ 2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by ₹ 20. How many students attended the picnic and how much did each student pay for the food?

If the price of a book is reduced by ₹ 5, a person can buy 4 more books for ₹ 600. Find the original price of the book.

A person on tour has ₹ 10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by ₹ 90. Find the original duration of the tour.  

In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained by him in the two subjects separately.

A man buys a number of pens for ₹ 180. If he had bought 3 more pens for the same amount, each pen would have cost him ₹ 3 less. How many pens did he buy?

A dealer sells an article for ₹ 75 and gains as much per cent as the cost priced of the article. Find the cost price of the article.

One year ago, man was 8 times as old as his son. Now, his age is equal to the square of his son’s age. Find their present ages.

The sum of reciprocals of Meena’s ages (in years ) 3 years ago and 5 years hence `1/3` Find her present ages. 

The sum of the ages of a boy and his brother is 25 years, and the product of their ages in years is 126. Find their ages.

The product of Tanvy’s age (in years) 5 years ago and her age is 8 years later is 30. Find her present age. 

 

Two years ago, man’s age was three times the square of his son’s age. In three years’ time, his age will be four time his son’s age. Find their present ages.  

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.

While boarding an aeroplane, a passengers got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30
minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed of the plane.
Do you appreciate the values shown by the pilot, namely promptness in providing help to
the injured and his efforts to reach in time?

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train. 

A train travels at a certain average speed for a distanced of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hr more, it would have taken 30 minutes less for the journey. Find the original speed of the train. 

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.

The distance between Mumbai and Pune is 192 km. Travelling by the Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speeds of the two
train differ by 20km/hr.

A motor boat whose speed in still water is 178 km/hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream

The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream is 5 hours. Fid the speed of the stream

A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream. 

A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

Two pipes running together can fill a cistern in `3 1/13` 
minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern. 

Two pipes running together can fill a tank in `11 1/9` minutes. If on pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank
separately.

Two water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately. Find the time which each tap can separately fill the tank.

The length of rectangle is twice its breadth and its areas is 288 cm  `288cm^2` . Find the dimension of the rectangle

The length of a rectangular field is three times its breadth. If the area of the field be 147 sq meters, find the length of the field.

The length of a hall is 3 meter more than its breadth. If the area of the hall is 238 sq meters, calculate its length and breadth. 

The perimeter of a rectangular plot is 62 m and its area is 288 sq meters. Find the dimension of the plot

A rectangular filed in 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 2 120m . Find the width of the path. 

The sum of the areas of two squares is `640m^2` . If the difference in their perimeter be 64m, find the sides of the two square 

The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. Their areas being equal, find the dimensions.

A farmer prepares rectangular vegetable garden of area 180 sq meters. With 39 meters of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden. 

The area of a right triangle is `600cm^2` . If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.

The area of right-angled triangle is 96 sq meters. If the base is three time the altitude, find the base. 

The area of right -angled triangle is 165 sq meters. Determine its base and altitude if the latter exceeds the former by 7 meters. 

 

The hypotenuse of a right=-angled triangle is 20 meters. If the difference between the lengths of the other sides be 4 meters, find the other sides 

The length of the hypotenuse of a right-angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle. 

The hypotenuse of a right-angled triangle is 1 meter less than twice the shortest side. If the third side 1 meter more than the shortest side, find the side, find the sides of the triangle.

Chapter 10: Quadratic Equations solutions [Page 0]

Which of the following is a quadratic equation? 

(a) `x^3-3sqrtx+2=0`                  (b) `x+1/x=x^2` 

(c)` x^2+1/x^2=5`                      (d) `2x^2-5x=(x-1)^2`

Which of the following is a quadratic equation? 

(a)` (x^2+1)=(2-x)^2+3`              (b)` x^3-x^2=(x-1)^3` 

(c) `2x^+3=(5+x)(2x-3)`                (d) None of these  

 

(a) `3x-x^2=x^2+5`                    (b) `(x+2)^2=2(x^2-5)` 

(c) `(sqrt2x+3)^2=2x^2+6`        (d)` (x-1)^2=3x^2+x-2`

If x=3 is a solution of the equation `3x^2+(k-1)x+9=0` then k=?  

(a) 11  (b)-11   (c)13   (d)-13   

If one root of the equation `2x^2+ax+6=0` 2 then a=?  

(a)7  (b)-7   (c) 7/2  (d)-7/2

The sum of the roots of the equation` x^2-6x+2=0` 

(a) 2 (b)-2  (c)6 (d)-6

If the product of the roots of the equation `x^2-3x+k=10`  is-2 then the value of k is
(a) -2 (b) -8 (c) 8 (d) 12   

The ratio of the sum and product of the roots of the equation `7x^2-12x+18=0` is 

(a) 7:12  (b)7:18  (c)3:2  (d)2:3 

If one root of the equation` 3x^2-10x+3=0  is  1/3` then the other root is  

(a) `-1/3`  (b) `1/3` (c)`-3` (d)`3` 

If one root of `5x^2+13x+k=0`  be the reciprocal of the other root then the value of k is  

`(a)0   (b)1   (c)2   (d)5` 

 

If the sum of the roots of the equation `kx^2+2x+3k=0` is equal to their product then the value of k 

`(a) 1/3   (b)-1/3  (c)2/3   (d)-2/3`  

 

 

The roots of a quadratic equation are 5 and -2. Then, the equation is 

(a)`x^2-3x+10=0`  (b)`x^2-3x-10=0` (c)x^2+3x-10=0 (d)`x^2+3x+10=0` 

 

If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is 

(a)`x^2-6x+6=0` (b)` x^2+6x+6=0` (c)`x^2-6x-6=0` (d)`x^2+6x+6=0`

If α and β are the roots of the equation `3x^2+8x+2=0` then (1/α+1/β)=? 

(a)` -3/8`   (b) `2/3`  `(c) -4  (d)4` 

 

 

The roots of the equation `ax^2+bx+c=0` will be reciprocal each other if 

(a)a=b (b)b=c (c)=a (d)= none of these 

If the roots of the equation` ax^2+bx+c=0` are equal then c=?   

(a)`b/(2a)`   (b) `b/(2a)`  (c) `-b^2/(4a)`  (d) `B^2/(4a)`

If the equation `9x^26kx+4=0`  has equal roots then k =? 

(a)1  or  (b)-1 or 4 (c)1 or -4  (d)-1 or -4 

If the equation `4x^2-3kx+1=0` has equal roots then value of k=?  

(a)`+-2/3`                     (b)`+-1/3` 

(c)` +-3/4`                     (d) `+-4/3` 

 

The roots of `ax^2+bx+c=0`,a≠0 are real and unequal, if  `(b^2-4ac)` is

(a)>0    (b)=0       (c)<0       (d)none of these 

In the equation `ax^2+bx+c=0` it is given that `D=(b^2-4ac)>0`  

equation are

(a) real and equal (b) real and unequal (c) imaginary (d) none of these

The roots of the equation 2x^2-6x+7=0  are

(a) real, unequal and rational (b) real, unequal and irrational (c) real and equal (d) imaginary 

The roots of the equation `2x^2-6x+3=0` are

(a) real, unequal and rational (b) real, unequal and irrational (c) real and equal (d) imaginary 

If the roots of` 5x^2-k+1=0` are real and distinct then  

(a)`-2sqrt5<k2<sqrt5`                     (b)` k>2sqrt5 ` only  

(c)` k<-2sqrt5`                              (d) either `k>2sqrt5  or  k<-2sqrt5`

If the equation `x^2+5kx+16=0` has no real roots then   

(a)`k>8/5`                          (b) `k(-8)/5`  

(c)` (-8)/5<k<8/5`                         (d)  None Of these

If the equation `x^2-5x+1=0` has no real roots then 

(a)`k<-2`

(b)`k>2` 

(c) `-2<k<2` 

(d)  None of these 

For what value of k, the equation `kx^2-6x2=0` has real roots?  

(a) `k≤-9/2`                     (b)`k≥-9/2` 

(c)` k≤-2`                         (d)  None of these 

The sum of a number and its reciprocal is `2 1/20` The number is  

(a) `5/4  or  4/5`                        (b)`4/3  or  3/4` 

(c) `5/6  or  6/5`                         (d) `1/6  or  6`

The perimeter of a rectangle is 82m and its area is  `400m^2` . The breadth of the rectangle is 

(a) 25m                (b)20m    

(c) 16m                 (d)9m

The length of a rectangular field exceeds its breadth by 8 m and the area of the field is `240 m^2` . The breadth of the field is

(a) 20 m (b) 30 m (c) 12 m (d) 16 m

The roots of the quadratic equation `2x^2-x-6=0` 

(a)`-2, 3/2`                           (b) `2, -3/2` 

(c)` -2, 3/2`                           (d) `2, 3/2` 

The sum of two natural numbers is 8 and their product is 15., Find the numbers. 

Show the x= -3 is a solution of `x^2+6x+9=0`

Show that x= -2  is a solution of `3x^2+13x+14=0` 

 

If `x=-1/2` is a solution of the quadratic equation  `3x^2+2kx-3=0` 

Find the value of k. 

Find the roots of the quadratic equation `2x^2-x-6=0` 

 

  • A.`-2,3/2`

  • B.`2,-3/2`

  • C.`-2,-3/2`

  • D.`2,3/2`

Find the solution of the quadratic equation `3sqrt3x^2+10x+sqrt3=0`

If the roots of the quadratic equation `2x^2+8x+k=0` are equal then find the value of k.  

If the quadratic equation `px^2-2sqrt5px+15=0`  has two equal roots then find the value of p.  

If 1 is a root of the equation `ay^2+ay+3=0`  and `y^2+y+b=0` then find the value of ab.  

If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` write the other zero. 

 

 

If one root of the quadratic equation `3x^2-10x+k=0` is reciprocal of the other , find the value  of k.  

 

If the roots of the quadratic equation `px(x-2)+=0` are equal, find the value of p. 

If the roots of the quadratic equation `px(x-2)+=0`  are equal, find the value of p

Find the value of k so that the quadratic equation` x^2-4kx+k=0` 

has equal roots. 

Find the value of k for which the quadratic equation `9x^2-3kx+k=0` has equal roots. 

 

Solve `x^2-(sqrt3+1)x+sqrt3=0`

Solve` 2x^2+ax-a^2=0`

Solve `3x^2+5sqrt5x-10=0`

Solve `sqrt3x^2+10x-8sqrt3=0`

Solve `sqrt3x^2-2sqrt2x-2sqrt3=0` 

 

Solve` 4sqrt3x^2+5x-2sqrt3=0`

Solve  `4x^2+4bx-(a^2-b^2)=0` 

Solve `x^2+5x-(a^2+a-6)=0` 

 

Solve `x^2+6x-(a^2+2a-8)=0` 

 

Solve` x^2-4ax+4a^2-b^2=0` 

Chapter 10: Quadratic Equations

R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

Secondary School Mathematics for Class 10 (for 2019 Examination) - Shaalaa.com

R.S. Aggarwal solutions for Class 10 Mathematics chapter 10 - Quadratic Equations

R.S. Aggarwal solutions for Class 10 Maths chapter 10 (Quadratic Equations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Secondary School Mathematics for Class 10 (for 2019 Examination) solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. R.S. Aggarwal textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 10 Quadratic Equations are Relationship Between Discriminant and Nature of Roots, Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated, Quadratic Equations Examples and Solutions, Quadratic Equations, Solutions of Quadratic Equations by Factorization, Solutions of Quadratic Equations by Completing the Square, Nature of Roots.

Using R.S. Aggarwal Class 10 solutions Quadratic Equations exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in R.S. Aggarwal Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer R.S. Aggarwal Textbook Solutions to score more in exam.

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