Find the value of k, if x − 1 is a factor of p(x) in each of the following cases:

(i) p(x) = x² + x + k (ii)

(iii) (iv) p(x) = kx² − 3x + k

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Solution

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

(i) p(x) = x² + x + k

p(1) = 0

⇒ (1)² + 1 + k = 0

⇒ 2 + k = 0

⇒ k = −2

Therefore, the value of k is −2.

(ii)

p(1) = 0

(iii)

p(1) = 0

(iv) p(x) = kx² − 3x + k

⇒ p(1) = 0

⇒ k(1)² − 3(1) + k = 0

⇒ k − 3 + k = 0

⇒ 2k − 3 = 0

Therefore, the value of k is.

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Find the value of k, if x − 1 is a factor of p(x) in each of the following cases: (i) p(x) = x2 + x + k (ii) (iii) (iv) p(x) = kx2 − 3x + k

Find the value of k, if x − 1 is a factor of p(x) in each of the following cases:

(i) p(x) = x² + x + k (ii)

(iii) (iv) p(x) = kx² − 3x + k