For what value of k, – 4 is a zero of the polynomial x2 – x – (2

1.	For what value of k, – 4 is a zero of the polynomial x2 – x – (2k + 2)?
Answer» Given, A polynomial x² – x – (2k + 2) – 4 is a zero of the given polynomial. As – 4 is the zero, so at x = -4, the value of the polynomial x² – x – (2k + 2) will be 0. So we get, ⇒x² – x – (2k + 2) = 0 ⇒(– 4)² – (– 4) – (2k + 2) = 0 ⇒16 + 4 – (2k + 2) = 0 ⇒20 – (2k + 2) = 0 ⇒ – (2k + 2) = – 20 ⇒2k + 2 = 20 ⇒ 2k = 20 - 2 ⇒2k = 18 ⇒ k = 18/2 = 9

For what value of k, – 4 is a zero of the polynomial x2 – x – (2k + 2)?

Answer»

Given, A polynomial

x² – x – (2k + 2)

– 4 is a zero of the given polynomial.

As – 4 is the zero,

so at x = -4,

the value of the polynomial

x² – x – (2k + 2) will be 0.

So we get,

⇒x² – x – (2k + 2) = 0

⇒(– 4)² – (– 4) – (2k + 2) = 0

⇒16 + 4 – (2k + 2) = 0

⇒20 – (2k + 2) = 0

⇒ – (2k + 2) = – 20

⇒2k + 2 = 20

⇒ 2k = 20 - 2

⇒2k = 18

⇒ k = 18/2 = 9