Question

Find the value of k, if x – 1 is a factor of p(x) in the following case:

p(x) = kx² – 3x + k

Answer 1

If x − 1 is a factor of polynomial p(x), then p(1) must be 0.

p(x) = kx² − 3x + k

⇒ p(1) = 0

⇒ k(1)² − 3(1) + k = 0

⇒ k − 3 + k = 0

⇒ 2k − 3 = 0

⇒ k = `3/2`

Therefore, the value of k is `3/2`.