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# Balbharati solutions for Class 10th Board Exam Algebra chapter 2 - Quadratic Equations

## Textbook for SSC Class 10 Mathematics 1

#### Chapter 2: Quadratic Equations solutions [Page 34]

Q 1 | Page 34

Q 2.1 | Page 34

Decide which of the following are quadratic equations.

x2 + 5– 2 = 0

Q 2.2 | Page 34

Decide which of the following are quadratic equations.

y= 5y – 10

Q 2.3 | Page 34

Decide which of the following are quadratic equations.

$y^2 + \frac{1}{y} = 2$

Q 2.4 | Page 34

Decide which of the following are quadratic equations.

$x + \frac{1}{x} = - 2$

Q 2.5 | Page 34

Decide which of the following are quadratic equations.

(m + 2) (– 5) = 0

Q 2.6 | Page 34

Decide which of the following are quadratic equations.

m+ 3m2 – 2 = 3m

Q 3.1 | Page 34

Write the following equations in the form ax2 + bx + c= 0, then write the values of abc for each equation.

2y = 10 – y

Q 3.2 | Page 34

Write the following equations in the form ax2 + bx + c= 0, then write the values of abc for each equation.

(x – 1)2 = 2x + 3

Q 3.3 | Page 34

Write the following equations in the form ax2 + bx + c= 0, then write the values of abc for each equation.

x2 + 5x = –(3 – x)

Q 3.4 | Page 34

Write the following equations in the form ax2 + bx + c= 0, then write the values of abc for each equation.

3m2 = 2m2 – 9

Q 3.6 | Page 34

Write the following equations in the form ax2 + bx + c= 0, then write the values of abc for each equation.

x2 – 9 = 13

Q 4.1 | Page 34

Determine whether the values given against each of the quadratic equation are the roots of the equation.

x2 + 4x – 5 = 0 , x = 1, –1

Q 4.2 | Page 34

Determine whether the values given against each of the quadratic equation are the roots of the equation.

2m2 – 5m = 0,

Q 5 | Page 34

Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0

Q 6 | Page 34

One of the roots of equation 5m2 + 2m + = 0 is $\frac{- 7}{5}$ Complete the following activity to find the value of 'k'.

#### Chapter 2: Quadratic Equations solutions [Pages 0 - 36]

Solve the following quadratic equations by factorisation.

x2 – 15x + 54 = 0

Solve the following quadratic equations by factorisation.

x2 + x – 20 = 0

Solve the following quadratic equations by factorisation.

2y2 + 27y + 13 = 0

Solve the following quadratic equations by factorisation.

5m2 = 22m + 15

Solve the following quadratic equations by factorisation.

2x2 – 2x +$\frac{1}{2}$=0

Solve the following quadratic equations by factorisation.

$6x - \frac{2}{x} = 1$

Solve the following quadratic equations by factorisation.

$\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0$  to solve this quadratic equation by factorisation, complete the following activity.

Solve the following quadratic equations by factorisation.

$3 x^2 - 2\sqrt{6}x + 2 = 0$

Solve the following quadratic equations by factorisation.

$2m\left( m - 24 \right) = 50$

Solve the following quadratic equations by factorisation.

$25 m^2 = 9$

Solve the following quadratic equations by factorisation.

$7 m^2 = 21m$

Solve the following quadratic equations by factorisation.

$m^2 - 11 = 0$

#### Chapter 2: Quadratic Equations solutions [Page 39]

Q 1.1 | Page 39

Solve the following quadratic equations by completing the square method.

x2 + x – 20 = 0

Q 1.2 | Page 39

Solve the following quadratic equations by completing the square method.

x2 + 2x – 5 = 0

Q 1.3 | Page 39

Solve the following quadratic equations by completing the square method.

m2 – 5m = –3

Q 1.4 | Page 39

Solve the following quadratic equations by completing the square method.

9y2 – 12y + 2 = 0

Q 1.5 | Page 39

Solve the following quadratic equations by completing the square method.

2y2 + 9y +10 = 0

Q 1.6 | Page 39

Solve the following quadratic equations by completing the square method.

5x2 = 4+ 7

#### Chapter 2: Quadratic Equations solutions [Pages 43 - 44]

Q 1.1 | Page 43

Compare the given quadratic equations to the general form and write values of a,bc

x2 – 7x + 5 = 0

Q 1.2 | Page 43

Compare the given quadratic equations to the general form and write values of a,bc.

2m2 = 5m – 5

Q 1.3 | Page 43

Compare the given quadratic equations to the general form and write values of a,bc

y2 = 7y

Q 2.1 | Page 43

Solve using formula.

x2 + 6x + 5 = 0

Q 2.2 | Page 43

Solve using formula.

x2 – 3x – 2 = 0

Q 2.3 | Page 43

Solve using formula.

3m2 + 2m – 7 = 0

Q 2.4 | Page 43

Solve using formula.

5m2 – 4m – 2 = 0

Q 2.5 | Page 43

Solve using formula.

$y^2 + \frac{1}{3}y = 2$

Q 2.6 | Page 43

Solve using formula.

5x2 + 13x + 8 = 0

Q 3 | Page 44

With the help of the flow chart given below solve the equation $x^2 + 2\sqrt{3}x + 3 = 0$ using the formula.

#### Chapter 2: Quadratic Equations solutions [Pages 49 - 50]

Q 1.1 | Page 49

Fill in the gaps and complete.

Q 1.2 | Page 49

Fill in the gaps and complete.

Q 1.3 | Page 49

Fill in the gaps and complete.

If α, β are roots of quadratic equation,

Q 2.1 | Page 49

Find the value of discriminant.

x2 + 7x – 1 = 0

Q 2.2 | Page 49

Find the value of discriminant.

2y2 – 5y + 10 = 0

Q 2.3 | Page 49

Find the value of discriminant.

$\sqrt{2} x^2 + 4x + 2\sqrt{2} = 0$

Q 3.1 | Page 49

Determine the nature of roots of the following quadratic equations.

x2 – 4x + 4 = 0

Q 3.2 | Page 49

Determine the nature of roots of the following quadratic equations.

2y– 7y +2 = 0

Q 3.3 | Page 49

Determine the nature of roots of the following quadratic equations.

m2 + 2m + 9 = 0

Q 4.1 | Page 50

Form the quadratic equation from the roots given below.

0 and 4

Q 4.2 | Page 50

Form the quadratic equation from the roots given below.

3 and –10

Q 4.3 | Page 50

Form the quadratic equation from the roots given below.

$\frac{1}{2}, - \frac{1}{2}$

Q 4.4 | Page 50

Form the quadratic equation from the roots given below.

$2 - \sqrt{5}, 2 + \sqrt{5}$

Q 5 | Page 50

Sum of the roots of a quadratic equation is double their product. Find k if equation x2 – 4kx + +3 = 0

Q 6.1 | Page 50

α, β are roots of y2 – 2y –7 = 0 find,

α2 + β

Q 6.2 | Page 50

α, β are roots of y2 – 2y –7 = 0 find,

α3 + β

Q 7.1 | Page 50

The roots of each of the following quadratic equations are real and equal, find k.

3y+ ky +12 = 0

Q 7.2 | Page 50

The roots of each of the following quadratic equations are real and equal, find k.

kx (x – 2) + 6 = 0

#### Chapter 2: Quadratic Equations solutions [Page 52]

Q 1 | Page 52

Product of Pragati’s age 2 years ago and 3 years hence is 84. Find her present age.

Q 2 | Page 52

The sum of squares of two consecutive natural numbers is 244; find the numbers.

Q 3 | Page 52

In the orange garden of Mr. Madhusudan there are 150 orange trees. The number of trees in each row is 5 more than that in each column. Find the number of trees in each row and each column with the help of following flow chart.

Q 4 | Page 52

Vivek is older than Kishor by 5 years. The sum of the reciprocals of their ages is $\frac{1}{6}$ Find their present ages.

Q 5 | Page 52

Suyash scored 10 marks more in second test than that in the first. 5 times the score of the second test is the same as square of the score in the first test. Find his score in the first test.

Q 6 | Page 52

Mr. Kasam runs a small business of making earthen pots. He makes certain number of pots on daily basis. Production cost of each pot is Rs 40 more than 10 times total number of pots, he makes in one day. If production cost of all pots per day is Rs 600, find production cost of one pot and number of pots he makes per day.

Q 7 | Page 52

Pratik takes 8 hours to travel 36 km down stream and return to the same spot. The speed of boat in still water is 12 km. per hour. Find the speed of water current.

Q 8 | Page 52

Pintu takes 6 days more than those of Nishu to complete certain work. If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone.

Q 9 | Page 52

If 460 is divided by a natural number, quotient is 6 more than five times the divisor and remainder is 1. Find quotient and diviser.

Q 10 | Page 52

In the adjoining fig. $\square$ ABCD is a trapezium AB || CD and its area is 33 cm2 . From the information given in the figure find the lengths of all sides of the $\square$ABCD. Fill in the empty boxes to get the solution.

#### Chapter 2: Quadratic Equations solutions [Pages 0 - 54]

Choose the correct answers for the following questions.
(1) Which one is the quadratic equation ?

(A)$\frac{5}{x} - 3 = x^2$                 (B) x(x+5)=2

(C)n-1=2n                                         (D)1/x^2(x+2)=x

Out of the following equations which one is not a quadratic equation ?

(A) x^2+4x=11+x^2                        (B) x^2=4x

(C)5x^2=90+5                                 (D) 2x-x^2=x^2

The roots of x2 + kx + k = 0 are real and equal, find k.

(A) 0                                                   (B)4

(C)0 or 4                                            (4)2

For $\sqrt{2} x^2 - 5x + \sqrt{2} = 0$ find the value of the discriminant.

(A)-5                                    (B)17

(C)sqrt2                             (D)2sqrt2-5

Which of the following quadratic equations has roots 3,5 ?

(A) x^2-15x+8=0                 (B)x^2-8x+15=0
(C)x^2+3x+5=0                   (D)x^2+8x-15=0

Out of the following equations, find the equation having the sum of its roots –5.

(A) 3x^2-15x+3=0              (B)x^2-5x+3=0

(C)x^2+3x-5=0                  (D)3x^2+15x+3=0

$\sqrt{5} m^2 - \sqrt{5}m + \sqrt{5} = 0$ which of the following statement is true for this given equation ?

(A) Real and uneual roots
(B)Real and equal roots
(C)Roots are not real
(D)Three roots.

One of the roots of equation x2 + mx – 5 = 0 is 2; find m.

(A) -2                        (B)-1/2

(C)1/2                      (D)2

Which of the following equations is quadratic ?

$x^2 + 2x + 11 = 0$

Which of the following equations is quadratic ?

$x^2 - 2x + 5 = x^2$

Which of the following equations is quadratic ?

$\left( x + 2 \right)^2 = 2 x^2$

Find the value of discriminant for each of the following equations.

$2 y^2 - y + 2 = 0$

Find the value of discriminant for each of the following equations.

$5 m^2 - m = 0$

Find the value of discriminant for each of the following equations.

$\sqrt{5} x^2 - x - \sqrt{5} = 0$

One of the roots of quadratic equation $2 x^2 + kx - 2 = 0$ is –2. find k

Two roots of quadratic equations are given ; frame the equation.

10 and –10

Two roots of quadratic equations are given ; frame the equation.

$1 - 3\sqrt{5} \text{ and } 1 + 3\sqrt{5}$

Two roots of quadratic equations are given ; frame the equation.

0 and 7

Determine the nature of roots for each of the quadratic equation.

$3 x^2 - 5x + 7 = 0$

Determine the nature of roots for each of the quadratic equation.

$\sqrt{3} x^2 + \sqrt{2}x - 2\sqrt{3} = 0$

Determine the nature of roots for each of the quadratic equation.

$m^2 - 4x - 3 = 0$

$\frac{1}{x + 5} = \frac{1}{x^2}$

$x^2 - \frac{3x}{10} - \frac{1}{10} = 0$

$\left( 2x + 3 \right)^2 = 25$

$m^2 + 5m + 5 = 0$

$5 m^2 + 2m + 1 = 0$

$x^2 - 4x - 3 = 0$

Find m if (m – 12) x2 + 2(–12) + 2 = 0 has real and equal roots.

The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.

Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation

$2 x^2 + 2\left( p + q \right)x + p^2 + q^2 = 0$

Mukund possesses Rs 50 more than what Sagar possesses. The product of the amount they have is 15,000. Find the amount each one has.

The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.

Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.

Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10 meter more than twice the breadth. In order to harvest rain water, he dug a square shaped pond inside the farm. The side of pond is $\frac{1}{3}$ of the breadth of the farm. The area of the farm is 20 times the area of the pond. Find the length and breadth of the farm and of the pond.

A tank fills completely in 2 hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes 3 hours more than the larger one to fill the tank. How much time does each tap take to fill the tank completely ?

## Balbharati solutions for Class 10th Board Exam Algebra chapter 2 - Quadratic Equations

Balbharati solutions for Class 10th Board Exam Algebra chapter 2 (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 Maharashtra State Board Textbook for SSC Class 10 Mathematics 1 solutions in a manner that help students grasp basic concepts better and faster.

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

Concepts covered in Class 10th Board Exam Algebra chapter 2 Quadratic Equations are Formula for Solving a Quadratic Equation, Roots of a Quadratic Equation, Solutions of Quadratic Equations by Completing the Square, Solutions of Quadratic Equations by Factorization, Relation Between Roots of the Equation and Coefficient of the Terms in the Equation Equations Reducible to Quadratic Form, Nature of Roots, Quadratic Equations, Quadratic Equations Examples and Solutions.

Using Balbharati Class 10th Board Exam 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 Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board Class 10th Board Exam prefer Balbharati Textbook Solutions to score more in exam.

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