Question

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

Answer 1

There could be 0, 2, or 4 complex solutions

Explanation:

The Fundamental Theorem of Algebra states that any polynomial with n degree will have n solutions So since the degree of the polynomial you provided has a degree of 4, that means there are 4 possible solutions. This question specifically asks for complex zeroes. Complex zeroes come in conjugate pairs, so that means if you have one complex zero, there is another complex zero which is it's conjugate. For this reason, there can only be an even number of complex zeroes. And since there's 4 possible solutions, There could be 0, 2, or 4 complex solutions