Which equation has roots -2c, 2c, and 2?

Question

This is a multiple choice question

1. $$-4c^2 -2c=0$$
2. $$-4c^2+2c=0$$
3. $$x^3 - 2x^2-4x+8=0$$
4. $$x^3 - 2x^2-4c^2x +8c^2=0$$

I know roots mean solutions, so do I plug in the given roots and see if they work?

I can't see how that would make sense. There are 3 roots given, so it can't be the 1st two because both of them have the power of 2, but the given are 3.

So I don't how should I solve this?

Answer 1

Several clues - you need a cubic for three roots, as you spotted. Of course you can plug in the given roots and see if they work. It is a multiple choice, so obviously there will be wrong answers. Eliminating obvious errors saves work.

A couple of other thoughts which may save work.

What is the product of the roots?

Or, as this is supposed to work for all $c$ - try putting $c=0$ and see what fits then.

Answer 2

Why not just multiply out $(x+2c)(x-2c)(x-2)$?