Question

What are the possible number of positive real, negative real, and complex zeros of

Answer 1

f(x) = −7x^4 − 12x^3 + 9x^2 − 17x + 3 you will have to change the signs so,
f(−x) = −7x^4 + 12x^3 + 9x^2 + 17x + 3

For positive roots, count number of times coefficients of f(x) change sign:
− − + − +
3 times -----> 3 or 1 positive roots

For negative roots, count number of times coefficients of f(−x) change sign:
− + + + +
1 time -----> 1 negative root

Positive real: 3 or 1
Negative real: 1
Complex non-real: 0 or 2

The answer is C

Answer 2

The answer is C :)
It can be properly explained by others below or above me