# Find the Value K If X − 3 is a Factor of K2x3 − Kx2 + 3kx − K. - Mathematics

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

#### Solution

Let f(x) = k^2 x^3 - kx^2 + 3kx - k be the given polynomial.

By the factor theorem,

(x − 3) is a factor of f(x) if f (3) = 0

Therefore,

f(3) = k^2 (3)^3 - k(3)^2 + 3k(3) - k = 0

$\Rightarrow 27 k^2 - 9k + 9k - k = 0$

$\Rightarrow 27 k^2 - k = 0$

$\Rightarrow k\left( 27k - 1 \right) = 0$

$\Rightarrow k = 0 \text { or k } = \frac{1}{27}$

Hence, the value of k is 0 or 1/27.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Exercise 6.4 | Q 13 | Page 24