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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) = `kx^2 - sqrt2x +1`
Sum
Solution
If x − 1 is a factor of polynomial p(x), then p(1) must be 0.
p(x) = `kx^2 - sqrt2x +1`
p(1) = 0
⇒ `k(1)^2 - sqrt2(1) + 1 = 0`
⇒ `k - sqrt2 + 1=0`
⇒ `k = sqrt2 - 1`
Therefore, the value of k is `sqrt2 -1`.
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Factorisation of Polynomials
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