Question

identify the roots and state the multiplicity of each root. -5x^3-20x^2+15x+90=0

Answer 1

The root -2 has a multiplicity of 1, and the root 3 has a multiplicity of 2.
The root 2 has a multiplicity of 1, and the root -3 has a multiplicity of 2.
or none of the above..

Answer 2

If you try a few numbers, you'll see that x=2 is a root, so x-2 can be factored out:

(x-2)(2nd deg polynomial)

With long division (or synthetic division) you can find out what the 2nd deg polynomial is.
It is: -5x^2-30x-45.
Factoring gives: -5(x^2+6x+9) = -5(x+3)^2, so the whole thing is:

-5(x-2)(x+3)^2, you can now see the roots and their multiplicities.