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

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Solution

If $(x - 1)$ is a factor of $p (x)$

Then $p (1) = 0$

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

$p (1) = k - 3 + k$

$0 = 2 k - 3$

So $k = \frac{3}{2}$ .

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Similar questions

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 of

k

, if

x - 1

is a factor of

p (x)

in each of the following cases:

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

Q. If

(x - 3)

is a factor of

p (x)

, find the value of

k

, Where

p (x) =

x^{2} - k^{2} x + k

Find the value of ‘k’ if x -1 is a factor of P(x) = 4 $x^{3}$ + $x^{2}$ – 3x + k.

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Find the value of k if x−1 is a factor of p(x) in the following case:p(x)=kx2−3x+k

If (x−1) is a factor of p(x)Then p(1)=0p(x)=kx2−3x+kp(1)=k−3+k0=2k−3So k=32.

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

If $(x - 1)$ is a factor of $p (x)$

Then $p (1) = 0$

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

$p (1) = k - 3 + k$

$0 = 2 k - 3$

So $k = \frac{3}{2}$ .