Find the value of k, if x - 1 is a factor of p(x)
$p (x) = k x^{2} - 3 x + k$

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Solution

(x -1) is a factor, so we substitute x = 1 in each case and solve for k by making p(1) equal to 0.
$p (x) = k x^{2} - 3 x + k p (1) = k - 3 + k = 0 \Rightarrow 2 k - 3 = 0 \Rightarrow k = \frac{3}{2}$

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

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

find the value of k if (x-1) is a factor of the polynomial kx²-3x+k

Find the value of k, if x − 1 is a factor of p(x) in each of the following cases:

(i) p(x) = x² + x + k (ii)

(iii) (iv) p(x) = kx² − 3x + k

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

Q. Find the value k if x − 3 is a factor of k²x³ − kx² + 3kx − k.

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Find the value of k, if x - 1 is a factor of p(x) p(x)=kx2−3x+k

(x -1) is a factor, so we substitute x = 1 in each case and solve for k by making p(1) equal to 0. p(x)=kx2−3x+kp(1)=k−3+k=0⇒2k−3=0⇒k=32

Find the value of k, if x - 1 is a factor of p(x)
$p (x) = k x^{2} - 3 x + k$

(x -1) is a factor, so we substitute x = 1 in each case and solve for k by making p(1) equal to 0.
$p (x) = k x^{2} - 3 x + k p (1) = k - 3 + k = 0 \Rightarrow 2 k - 3 = 0 \Rightarrow k = \frac{3}{2}$