Question

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

Answer 1

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

Explanation:

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`