Question

What are the possible number of positive real, negative real, and complex zeros of
f(x) = -7x4 - 12x3 + 9x2 - 17x + 3?

Positive Real: 3 or 1
Negative Real: 1
Complex: 2 or 0


Positive Real: 3 or 1
Negative Real: 2 or 0
Complex: 1


Positive Real: 1
Negative Real: 3 or 1
Complex: 2 or 0


Positive Real: 4, 2 or 0
Negative Real: 1
Complex: 0 or 1 or 3

I think its

Positive Real: 4, 2 or 0
Negative Real: 1
Complex: 0 or 1 or 3

but I feel like I am wrong.

Answer 1

look up Descartes rule of signs for the real roots. and once you find them if you can get it to quadratic form use the quadratic formula to get the complex roots.