Question

A polynomial has a degree of 9, and Mary Jane claims that it has exactly 4 real zeros. Can her claim be correct? Why or why not?

A) No, her claim cannot be correct. A polynomial of degree 9 must have 9 real or 9 nonreal solutions.
B) Yes, her claim can be correct. If a polynomial with degree 9 has 4 real solutions then it will have 5 nonreal solutions.
C) Yes, her claim can be correct. A polynomial with degree 9 can have at most 9 solutions, therefore having 4 real solutions is a possibility.
D) No, her claim cannot be correct. If a polynomial with degree 9 has 4 real solutions then it must have 5 nonreal solutions, which is not possible.

Answer 1

The number of zeroes of a polynomial should be equal to its degree. This means that for a polynomial of degree 9, there should be 9 roots or zeroes. The number of nonreal roots should be even since they come mostly in pairs. Therefore the answer to this item is letter D.