Question

What are the possible number 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

Answer 1

i give medals . (:

Answer 2

3 sign changes in f(x) --> 1 or 3 positive zeros

1 sign change in f(-x) --> 1 negative zero

4 total zeros --> 0 or 2 imaginary zeros

Answer 3

do synthetic division
4 power means you have 4 solutions
also, complex solutions come in pairs