If $(x - 3)$ is a factor of $p (x)$ , find the value of $k$ , Where $p (x) =$ $x^{2} - k^{2} x + k$

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Solution

$(x - 3)$ is a factor of $p (x)$ .
$p (x) = x^{2} - k^{2} x + k$
$p (3) = 0$
$⟹ (- 3)^{2} - k^{2} (3) + k = 0 ⟹ 3 k^{2} - k - 9 = 0$
solving this equation using quadratic formula
$k = \frac{1 \pm \sqrt{1^{2} - 4 (3) (- 9)}}{6}$
$k = \frac{1 \pm \sqrt{109}}{6}$

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Q. If

x - 1

is factor of

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

Find the value of

k

Q. Find the value of

k

, if

x - 1

is a factor of

p (x)

in each of the following cases

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

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 of P(x) = 4 $x^{3}$ + $x^{2}$ – 3x + k.

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If (x−3) is a factor of p(x) , find the value of k , Where p(x)=x2−k2x+k

(x−3) is a factor of p(x).p(x)=x2−k2x+kp(3)=0⟹(−3)2−k2(3)+k=0⟹3k2−k−9=0solving this equation using quadratic formula k=1±√12−4(3)(−9)6k=1±√1096

If $(x - 3)$ is a factor of $p (x)$ , find the value of $k$ , Where $p (x) =$ $x^{2} - k^{2} x + k$

$(x - 3)$ is a factor of $p (x)$ .
$p (x) = x^{2} - k^{2} x + k$
$p (3) = 0$
$⟹ (- 3)^{2} - k^{2} (3) + k = 0 ⟹ 3 k^{2} - k - 9 = 0$
solving this equation using quadratic formula
$k = \frac{1 \pm \sqrt{1^{2} - 4 (3) (- 9)}}{6}$
$k = \frac{1 \pm \sqrt{109}}{6}$