A polynomial of degree 4 can have how many real zeros? (what about a degree of 5)?

Answer 1

The answer is 4. In general, a polynomial of degree N can have no more than N zeroes. So a polynomial of degree 5 can have more than 5 zeroes.

This includes both real and complex zeroes. But you can always construct an N-degree polynomial with N real zeroes by taking (x - 1)(x - 2)(x - 3)...(x - N) and multiplying everything out. The zereos of this would obviously be 1, 2, 3, etc.

Answer 2

I think that geezah meant to say that the order 5 poly can have no more than 5 zeros.

An odd order polynomial must have at least one real zero.

Answer 3

The Fundamental Theorem of Algebra (yes, it's a big one) says that a polynomial of nth negree has n complex zeros, including multiplicities.