If $kx^3-kx+9$ is divisible by $x-1$ , then what is $k$ ?

Question

1484 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-13T00:55:34

$k = 1/2+-sqrt(35)/2i$

Given:

$f(x) = k^2x^3-kx+9$

If $f(x)$ is divisible by $(x-1)$ then $f(1) = 0$ , so:

$0 = f(1) = k^2-k+9$

Solving for $k$ using the quadratic formula we find:

$k = (1+-sqrt((-1)^2-4(1)(9)))/(2(1))$

$color(white)(k) = (1+-sqrt(1-36))/2$

$color(white)(k) = 1/2+-sqrt(35)/2i$

If kx^3-kx+9kx^3-kx+9 is divisible by x-1x-1, then what is kk?