A few quick C1 questions...

firstly, b^2-4ac > 0 for two distinct roots.
second, you shouldn't assume it is true and follow through by manipulating an equation. as a proof, you should take b^2-4ac, substitute in, rearrange it and show that it is positive irregardless of k. writing it as an equation leads you to do things like multiply by -1, which is silly because now you have 4ac-b^2, not what you want.

I do agree that the question looks like it was writen wrongly.

firstly, b^2-4ac > 0 for two distinct roots.
second, you shouldn't assume it is true and follow through by manipulating an equation. as a proof, you should take b^2-4ac, substitute in, rearrange it and show that it is positive irregardless of k. writing it as an equation leads you to do things like multiply by -1, which is silly because now you have 4ac-b^2, not what you want.

I do agree that the question looks like it was writen wrongly.

it is a quadratic function.
see the k^2.