Question

What are the possible numbers of positive, negative, and complex zeros of f(x) = 3x4 − 5x3 − x2 − 8x + 4?

Answer 1

Two positive zeros, no negative zeros, two complex roots.

Explanation:

The given function is
`f(x)=3x^4-5x^3-x^2-8x+4`

According to the fundamental theorem of algebra, the function will have 4 roots.

The graph of the function intersects the positive axis at two points.

Hence the function has two positive zeros and no negative zeros.

The two remaining roots are imaginary. The function has two complex zeros.

See graph in attachment