Find the value of k, if x – 1 is a factor of p(x) in the following case:- p(x) = x2 + x + k
If x − 1 is a factor of polynomial p(x), then p(1) must be 0.
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.
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