Find the value of k if x -3 is a factor of $k^{2} x^{3} - k x^{2} + 3 k x - k$ .

Open in App

Solution

Consider given the expression ,

$k^{2} x^{3} - k x^{2} + 3 k x - k$

Also given that,

$x - 3$ or $x - 3 = 0 \Rightarrow x = 3$ is factor of $k^{2} x^{3} - k x^{2} + 3 k x - k$

So,

$k^{2} 3^{3} - k {.3}^{2} + 3 k 3 - k = 0$

$27 k^{2} - 9 k + 9 k - k = 0$

$27 k^{2} - k = 0$

$k (27 k - 1) = 0$

$k = 0 o r 27 k - 1 = 0$

$k = 0 o r k = \frac{1}{27}$

Hence, this is the answer.

Suggest Corrections

Similar questions

Find the value k where x-3id a factor of k²x³-kx²+3kx-k.

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

Q. If

x - 2

is a factor of

k x^{2} - \sqrt{2} x + 1

, then find the value of

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

Join BYJU'S Learning Program

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

Consider given the expression , k2x3−kx2+3kx−k Also given that, x−3or x−3=0⇒x=3 is factor of k2x3−kx2+3kx−k So, k233−k.32+3k3−k=0 27k2−9k+9k−k=0 27k2−k=0 k(27k−1)=0 k=0or27k−1=0 k=0ork=127 Hence, this is the answer.

Find the value of k if x -3 is a factor of $k^{2} x^{3} - k x^{2} + 3 k x - k$ .