Find the value of 𝑘, if − 1 is one of the zeros of the polynomial

𝑝(𝑥) = 𝑘𝑥² − 4𝑥 + 𝑘.

We are given that − 1 is a zero of the polynomial 𝑝(𝑥) = 𝑘𝑥² − 4𝑥 + 𝑘, and we have to find the value of 𝑘.

As − 1 is a zero of the polynomial, on putting − 1 in place of 𝑥, the value of the polynomial will become zero, i.e.,

𝑝(− 1) = 0

⇒ 𝑘(− 1)² − 4 × (− 1) + 𝑘 = 0

⇒ 𝑘 × 1 + 4 + 𝑘 = 0

⇒ 𝑘 + 𝑘 + 4 = 0

⇒ 2𝑘 + 4 = 0

⇒ 2𝑘 =− 4

⇒ 𝑘 = -4/2

⇒ 𝑘 =− 2

Hence, the value of 𝑘 is − 2.