Question

What are the possible number of positive,negative,and complex zeros of f(x)=3x^4-5x^3-x^2-8x+4

Answer 1

Use Descartes' Rule of Signs to get the possible number of positive and negative real roots.

Answer 2

Attached are the results from the online calculator at:

http://www.emathhelp.net/calculators/algebra-1/descartes-rule-of-signs-calculator/

Answer 3

There are 2 or 0 positive Real roots.

There are 2 or 0 negative Real roots.

There are 4 or 2 or 0 nonReal roots.
(The Fundamental Theorem of Algebra states that there are 4 roots of some ilk. Non Real roots come in conjugate pairs. That's how to know the nonReal but Complex root possibilities.

Answer 4

Let's set up a chart showing the root possibilities

Real NonReal
Positive Negative
----------------------------------------------
0 0 4

2 0 2

0 2 2

2 2 0

Answer 5

Though you are not asked, I thought you'd like to know which one of these possibilities is what happens with f(x)=3x^4-5x^3-x^2-8x+4.

Two positive Real roots and 2 NonReal (Complex) roots.

@Rainytea101

Answer 6

welcome to os