Question

What are the possible numbers of positive, negative, and complex zeros of f(x) = x6 + x5 + x4 + 4x3 − 12x2 + 12?

Answer 1

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

Explanation:

Answer 2

As per Descartes Theorem, a polynomial of degree n (n is the highest exponent of a polynomial) has n roots (or number of zeros) be it positive, negative, real or complex.

in f(x) = x⁶ + x⁵ + x⁴ + 4x³ − 12x² + 12, the highest degree is 6, then it has
a total of 6 zeros, positive, negative, real or complex.