Question

What are the possible number of positive, negative, and complex zeros of f(x) = -2x^3 + 5x^2 - 6x + 4 ?




A.Positive: 3 or 1; Negative: 1; Complex: 2 or 0
B.Positive: 1; Negative: 2 or 0; Complex 2 or 0
C.Positive: 2 or 0; Negative: 1; Complex: 2 or 0
D.Positive: 3 or 1; Negative: 0; Complex: 2 or 0

Answer 1

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For the number of positive roots look at the number of sign changes from term to term. In this case the terms are -, +, -, + That's a total of 3 sign changes. Therefor there are 3 or 1 positive roots.

For negative roots you plug in a -x into the function and get a new function, then find the number of sign changes in that one. In this case, the new function is +,+,+,+ so no sign changes, so no negative roots.

The answer is D.