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Find the value of k, if x-1 is a factor of p(x) in each of the

Question

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

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Harper Discussed

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

(ii)

p (x) = 2 x^{2} + k x + 2

(iii)

p (x) = k x^{2} - 2 x + 1

(iv)

p (x) = k x^{2} - 3 x + k

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Text solutionVerified

x - 1

is the factor of the equation then put

x = 1

in these equation

(i)

x^{2} + x + k = 0 \Rightarrow (1)^{2} + 1 + k = 0 \Rightarrow 1 + 1 + k = 0 \Rightarrow k = - 2

(ii)

2 x^{2} + k x + 2 = 0 \Rightarrow 2 (1)^{2} + k (1) + 2 = 0 \Rightarrow 2 + k + 2 = 0 \Rightarrow k = - 2 - 2

(iii)

k x^{2} - 2 x + 1 = 0 \Rightarrow k (1)^{2} - 2 (1) + 1 = 0 \Rightarrow k - 2 + 1 = 0 \Rightarrow k = 2 - 1

(iv)

k x^{2} - 3 x + k = 0 \Rightarrow k (1)^{2} - 3 (1) + k = 0 \Rightarrow k - 3 + k = 0 \Rightarrow 2 k = - 3 \Rightarrow k = - \frac{3}{2}

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Question Text	Find the value of $k$ , if $x - 1$ is a factor of $p (x)$ in each of the following cases: (i) $p (x) = x^{2} + x + k$ (ii) $p (x) = 2 x^{2} + k x + 2$ (iii) $p (x) = k x^{2} - 2 x + 1$ (iv) $p (x) = k x^{2} - 3 x + k$
Answer Type	Text solution:1
Upvotes	150