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Question 4 What are the roots of the polynomial P(x)=2x^(4)-4x^(3)-16x^(2) ? Select all that apply.

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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.

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