Question

What are the possible number of positive real, negative real, and complex zeros of
f(x) = -7x^4 - 12x^3 + 9x^2 - 17x + 3?

Answer 1

There is a theorem in algebra which says that for a degree n polynomial with real coefficients there are exactly n complex roots (some possibly with no imaginary part, i.e., they are real).

That is a degree 4 polynomial. So there are exactly 4 complex roots.

Answer 2

W|A tells me it has 2 real roots and 2 complex roots (i.e 4 complex roots)

Answer 3

but that's not one of the options given? here are the options
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

Answer 4

You're told that it has 2 complex roots, so A and C satisfies this. Now W|A told me it has 1 positive real root and 1 negative real roots.

If you're doing homework, W|A is a very useful tool.

Answer 5

i'm confused.

Answer 6

Plug this equation into wolframalpha.com

Answer 7

it doesn't say anything about this?

Answer 8

From the attached plot there is one real negative root and one real positive root.