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