What are the possible number of positive real, negative real, and complex zeros of f(x) = 4x3 + x2 + 10x – 14?

a.) positive real: 1. negative real: 0. complex: 2
b.) positive real: 1. negative real: 2 or 0. complex: 2 or 0
c.) positive real: 2 or 0. negative real: 1. complex: 2 or 0
d.) positive real: 2 or 0. negative real: 2 or 0. complex: 1

f(0) = -14 is easy to calculate. You can actually note that other than -14, every coefficient are positive, so f will be increasing for x > 0 and it will eventually hit zero, turn positive, and continue on getting larger. So it has exactly 1 positive real root. So this means that it only has exactly 1 positive real root and these would be the possible numbers of positive real, negative real, and complex zeros of f(x) = 4x3 + x2 + 10x – 14.

Positive Real: 1.

Negative Real: 2 or 0.

Complex: 2 or 0 

The correct answer between all the choices given is the second choice or letter B. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.