Question

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

Answer 1

Descartes' Rule of Signs tells you there could be two positive and two negative roots, but either of those pair of roots could be replaced by a pair of complex conjugates.

In actuality, that function has two positive and two complex roots.

Answer 2

answers:
Positive: 2 or 0; Negative: 2 or 0; Complex: 4 or 2 or 0
Positive: 2 or 0; Negative: 2 or 0; Complex: 4 or 2
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