Question

If ‒4 is a zero of the polynomial x² ‒ x- (2k + 2) then find the value of k.

Answer 1

In the given polynomial f(x) = x² − x − (2k + 2), substitute x = −4 as shown below:

f(−4) = (−4)² − (−4) − (2k + 2) 

= 16 + 4 − 2k − 2

= 18 − 2k

Therefore, f(−4) = 18 − 2k.

Since it is given that x = −4 is a zero of the polynomial f(x) = x² − x − (2k + 2), therefore f(−4) = 0 that is:

18 − 2k = 0

⇒ 2k = 18

⇒ k = 18​/2

⇒ k = 9

Hence k = 9.

Answer 2

Given: -4 is one of zeroes of the polynomial x² ‒ x- (2k + 2), which means x = -4 will satisfy it.

x² – x – (2k + 2) = 0

(-4)^2 – (-4) – 2k – 2 = 0

16 + 4 – 2k – 2 = 0

-2k + 18 = 0

k = 9

The value of k is 9.