Question

show that 1/2 is a zero of g(x)= 2(x)²+7x-4​

Answer 1

Step-by-step explanation:

g(x) = 2x²+7x-4

Method 1 :

Substitute x = 1/2

=> g(1/2) = 2(1/2)² + 7(1/2) - 4

=> g(1/2) = 1/2 + 7/2 - 4

=> g(1/2) = 8/2 - 4

=> g(1/2) = 0

Method 2 :

Factorize g(x)

g(x) = 2x²+7x-4

= (1/2) ( x² + (7/2) x - 2 )

= (1/2) ( x² + 4x - (1/2)x - 2 )

= (1/2) ( x ( x + 4 ) - ((1/2)( x + 4))

= (1/2) ( x + 4 ) ( x - 1/2 )

g(x) = (1/2) ( x + 4 ) ( x - 1/2 )

Hence, for x = 1/2 and x = -4, g(x) = 0