Find the value of k, if x - 1 is a factor p(x) in each of the following cases:
(i) $p (x) = x^{2} + x + k$
(ii) $p (x) = 2 x^{2} + k x + \sqrt{2}$
(iii) $p (x) = k x^{2} - \sqrt{2} x + 1$
(iv) $p (x) = k x^{2} - 3 x + k$

Find the value of k, if (x −1) is a factor of p(x) in each of the following cases:
$(i) p (x) = x^{2} + x + k$
$(i i) p (x) = {2 x}^{2} + k x + \sqrt{2}$ [4 MARKS]

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If (x−1) is a factor of p(x)=x2+x+k, then value of k is :

The correct option is C −2Given: quadratic equation x2+x+k, (x−1) is a factorTo find the value of kSol: As (x−1) is a factor of the equation, ⇒x=1 is one of the root, then (1)2+1+k=0 should be satisfied,i.e., 1+1+k=0⇒k=−2

If $(x - 1)$ is a factor of $p (x) = x^{2} + x + k$ , then value of k is :

The correct option is C $- 2$
Given: quadratic equation $x^{2} + x + k$ , $(x - 1)$ is a factor
To find the value of k
Sol: As $(x - 1)$ is a factor of the equation, $\Rightarrow x = 1$ is one of the root, then
$(1)^{2} + 1 + k = 0$ should be satisfied,
i.e., $1 + 1 + k = 0 \Rightarrow k = - 2$