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Question
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = `2x^2+kx+sqrt2`
Solution
If x − 1 is a factor of polynomial p(x), then p(1) must be 0.
p(x) = `2x^2+kx+sqrt2`
p(1) = 0
⇒ `2(1)^2 + k(1) + sqrt2 = 0`
⇒ `2 + k + sqrt2 = 0`
⇒ k = `-2 -sqrt2`
k = `-(2+sqrt2)`
Therefore, the value of k is `-(2+sqrt2)`.
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