Question

1.Find the roots of the following quadratic equation by factorization: a) 100x2-20x+1=0 b)6x2-x-2=0 c) 2x2+x-300=0

Answer 1

Solution:

a). 100x2 - 20x + 1 = 0

= 100x2 - 10x - 10x + 1 = 0

= 10x ( 10x - 1 ) - 1 ( 10x - 1 ) = 0

= ( 10x - 1 ) ( 10x - 1 ) = 0

so, the roots of the given equation are x = 1/10 or x= 1/10

b). 6x2 - x - 2 = 0

= 6x2 - 4x + 3x - 2 = 0

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

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

so, the roots of the given equation are x = -1/2 ,2/3

c). 2x2 + x - 300 = 0

= 2x2 - 24x + 25x - 300 = 0

= 2x ( x - 12 ) + 25 ( x - 12 ) = 0

= ( 2x + 25 ) ( x - 12 ) = 0

so, the roots of the given equation are x = - 12.5 , 12