What are the possible numbers of positive, negative, and complex zeros of f(x) = −x^6 + x^5 − x^4 + 4x^3 − 12x^2 + 12?

Positive: 4, 2, or 0; negative: 2 or 0; complex: 6, 4, 2, or 0

Positive: 3 or 1; negative: 3 or 1; complex: 4, 2, or 0

Positive: 2 or 0; negative: 2 or 0; complex: 6, 4, or 2

Positive: 5, 3, or 1; negative: 1; complex: 4, 2, or 0

Question

What are the possible numbers of positive, negative, and complex zeros of f(x) = −x^6 + x^5 − x^4 + 4x^3 − 12x^2 + 12?

Positive: 4, 2, or 0; negative: 2 or 0; complex: 6, 4, 2, or 0

Positive: 3 or 1; negative: 3 or 1; complex: 4, 2, or 0

Positive: 2 or 0; negative: 2 or 0; complex: 6, 4, or 2

Positive: 5, 3, or 1; negative: 1; complex: 4, 2, or 0

anonymous · Answer

I know that you need to use the Descartes Rule or something like that, but I dont know how.

welshfella · Answer

yeah you look for changes of signs

anonymous · Answer

Can you help me find the answer?

welshfella · Answer

anonymous · Answer

So 5 sign changes, now what can I do with that information?

mathstudent55 · Answer

How many changes of signs do you see?
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