Question

If x = 2 is a root of the polynomial f (x)= 2x² - 3x + 7a, find the value of a.

Answer 1

We have,

f (x) = 2x² – 3x + 7a

Put x = 2

f (2) = 2 (2)² – 3 (2) + 7a

= 2 x 4 – 6 + 7a

= 8 – 6 + 7a

= 2 + 7a

Given, 

x = 2 is a root of f (x) = 2x² – 3x + 7a

f (2) = 0

Therefore, 

2 + 7a = 0

7a = -2

a = \(\frac{-2}{7}\)