To find the roots of the polynomial P(x)=2x^4 - 4x^3 - 16x^2, first divide by 2x^2 in order to simplify the equation:
P(x)=x^2 - 2x - 8 = 0
This equation is now quadratic and can be solved by factoring:
(x - 4)(x + 2) = 0
Setting each factor equal to zero gives the solutions x = 4 and x = -2.
However, don't forget that we initially divided our polynomial by 2x^2. Thus, x = 0 is also a root of the original polynomial.
So, the roots of the polynomial are x = -2, x = 0, and x = 4.