Question

What are the possible number of positive, negative, and complex zeros of f(x) = 2x3 + 5x2 + 6x - 4 ?

Positive: 2 or 0; Negative: 1; Complex: 2 or 0
Positive: 1; Negative: 2 or 0; Complex 2 or 0
Positive: 2 or 1; Negative: 1; Complex: 2 or 0
Positive: 1; Negative: 2 or 0; Complex: 0

Answer 1

f(x) changes sign how many times?

Answer 2

f(x) = 2x^3 - 5x^2 + 6x - 4
There are 3 or 1 possible positive zeros.

f(-x) = -2x^3 - 5x^2 - 6x - 4
There are no possible negative zeros.

There are possibly 2 complex zeros.

Answer 3

f(x) = 2x3 + 5x2 + 6x - 4
1 | 0

ther eis only 1 sign change; so there is 1 positive root

Answer 4

and the only difference between the 1 positive options is a complex or not

if there are 2 or 0; that implies complex roots as well