हिंदी

Show that X = −2 is a Solution of 3x2 + 13x + 14 = 0. - Mathematics

Advertisements
Advertisements

प्रश्न

Show that x = −2 is a solution of 3x2 + 13x + 14 = 0.

संक्षेप में उत्तर
Advertisements

उत्तर

Given that the equation  3x2 + 13x + 14 = 0

     `3x^2 + 7x + 6x + 14 = 0`

`x (3x + 7) + 2 (3x + 7) = 0`

            `(3x + 7) (x + 2) = 0`

(3x + 7) = 0

`x = (-7)/3`

 or

(x + 2) = 0

 x = - 2

Therefore, x = -2 is the solution of given equation.

Hence, proved.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Quadratic Equations - Exercise 4.14 [पृष्ठ ८२]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 10
अध्याय 4 Quadratic Equations
Exercise 4.14 | Q 13 | पृष्ठ ८२

संबंधित प्रश्न

Solve for x :

`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`

 


A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.


A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.


Solve the following quadratic equations by factorization:

(a + b)2x2 - 4abx - (a - b)2 = 0


The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.


Solve each of the following equations by factorization: 

`2x^2-1/2x=0` 


Solve each of the following equations by factorization : 

`6/x=1+x` 

 


`7x^2+3x-4=0` 


Find the values of k for which the roots are real and equal in each of the following equation:

\[kx\left( x - 2\sqrt{5} \right) + 10 = 0\]


Solve the following equation : `"x"^2 - 4 sqrt 2 "x" + 6 = 0 `


Solve the following equation :

`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6` 


Solve the following equation:  `x^2 + (a + 1/a)x + 1 = 0`


The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.


A farmer wishes to grow a 100m2 rectangular vegetable garden. Since he was with him only 30m barbed wire, he fences 3 sides of the rectangular garden letting the compound of his house to act as the 4th side. Find the dimensions of his garden .


Solve equation using factorisation method:

2x2 – 9x + 10 = 0, when:

  1. x ∈ N
  2. x ∈ Q

Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:

  1. the age of the son five years ago.
  2. the present age of the woman.

In each of the following determine whether the given values are solutions of the equation or not.
9x2 - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`


A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.


Rs. 7500 is divided equally among a certain number of children. Had there been 20 less children, each would have receive Rs 100 more. Find the original number of children. 


Complete the following activity to solve the given quadratic equation by factorization method.

Activity: x2 + 8x – 20 = 0

x2 + ( __ ) – 2x – 20 = 0

x (x + 10) – ( __ ) (x + 10) = 0

(x + 10) ( ____ ) = 0

x = ___ or x = 2


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×