Question

What are the possible numbers of positive, negative, and complex zeros of f(x) = -3x4 + 5x3 - x2 + 8x + 4?

Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
Positive: 1; negative: 3 or 1; complex: 2 or 0
Positive: 3 or 1; negative: 1; complex: 2 or 0
Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
Can you plz help me? @jim_thompson5910

Answer 1

Recall Descartes rule of signs.
How many times has the polynomial changed signs?

Answer 2

The number of sign changes of the polynomial is the maximum number of positive roots, reduced by the actual number of complex roots, if any.