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


a)positive real: 1
negative real: 3 or 1
complex: 2 or 0

b)positive real: 3 or 1
negative real: 2 or 0
complex: 1

c)positive real: 3 or 1
negative real: 1
complex: 2 or 0

d)positive real: 4, 2 or 0
negative real: 1
complex: 0 or 1 or 3

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