If one factor of x3 + 7kx2 - 4kx + 12 is (x + 3), then the value of k - Maths - Polynomials

Question

If one factor of x3 + 7kx2 - 4kx + 12 is (x + 3),
then the value of k is

Ajanta Trivedi · Accepted Answer

let the given polynomial be $f (x) = x^{3} + 7 k x^{2} - 4 k x + 12$

if (x+3) is a factor of f(x).

put x+3=0 i.e. x = -3

therefore by the factor theorem:

$f (- 3) = 0 (- 3)^{3} + 7 k * (- 3)^{2} - 4 k * (- 3) + 12 = 0 - 27 + 63 k + 12 k + 12 = 0 75 k - 15 = 0 75 k = 15 \Rightarrow k = \frac{15}{75} = \frac{1}{5}$

thus the value of k is 1/5.

hope this helps you.

cheers!!

If one factor of x3 + 7kx2 - 4kx + 12 is (x + 3), then the value of k is