Explain why a function is defined by a polynomial of degree 4 with real coefficients has either zero, two, or four real zeros (counting multiplications).

Question

Explain why a function is defined by a polynomial of degree 4 with real coefficients has either zero, two, or four real zeros (counting multiplications).

Answer 1

A polynomial of degree four can have a maximum of four zeros. If it has complex zeros, these always come in sets of two. Example: 1 +or- 3i. Therefore, you can have four real zeros, two real zeros and two complex zeros, or no real zeros and four complex zeros.