Question

Which of the following is a root of P(x)=-2x^3+x^2+4x+4? -1 0 1 2

Answer 1

Answer:

  2

Step-by-step explanation:

You know 0, 1, and -1 are not roots, because the constant is not 0 and the coefficients don't add to 0, even when negating the ones of odd-degree terms.

When evaluating polynomials by hand, it often works well to write them in "Horner form."

  P(x) = ((-2x +1)x +4)x +4

  P(2) = ((-2·2 +1)2 +4)2 +4 = (-3·2 +4)2 +4 = -2·2 +4

  P(2) = 0

2 is a root of P(x).

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I like a graphing calculator for questions like this. It can give an answer instantly. (The equation was pasted directly from the question into the calculator, so the solution took 2 clicks and 2 keystrokes.)