Question

Solve the following quadratic equations by factorization :

a) x²+6x+5=0

b) 8x²-22x-21=0

c) 9x²-3x-2=0

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Answer 1

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A)

Given quadratic equation is x²+6x+5=0

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,

Here, a = 1 , b= +6, c=+5

x²+6x+5=0

x²+x+5x+5=0

xx+1+5x+1

(x+5)(x+1)

x=-5 x=-1

Hence, roots of equation x²+6x+5=0 are -5 & -1

B)

Given quadratic equation is 8x² - 22x - 21= 0.

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,

Here, a = 8 , b= -22 , c= -21

8x² - 22x - 21= 0

8x² - 28x +6x  -21=0

4x (2x - 7) + 3(2x -7)= 0

(4x+3) ( 2x-7) = 0

(4x+3) = 0   or  ( 2x-7) = 0

4x = 0-3   or 2x= 0+7

x = -¾,    x = 7/2

Hence, roots of equation 8x² - 22x - 21= 0 are -¾ and 7/2.

C)

Given quadratic equation is 9x² - 3x - 2 = 0

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,

Here, a = 9 , b= -3 , c= -2

9x² - 3x - 2 = 0

9x² - 6x + 3x  -2 = 0

3x (3x - 2) + 1(3x - 2) = 0

(3x - 2)(3x + 1) = 0

3x - 2   or  3x + 1 = 0  

3x = 2  or  3x = - 1

x = ⅔   or  x = -1/3

Hence, the roots of the quadratic equation 9x² - 3x - 2 = 0 are ⅔ and -⅓ .

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