Question

If a polynomial is of a degree of n how many real zeros can it have?

Answer 1

See explanation...

Explanation:

Assuming the polynomial is non-constant and has Real coefficients, it can have up to `n` Real zeros.

If `n` is odd then it will have at least one Real zero.

Since any non-Real Complex zeros will occur in Complex conjugate pairs the possible number of Real roots counting multiplicity is an even number less than `n`.

For example, counting multiplicity, a polynomial of degree `7` can have `7`, `5`, `3` or `1` Real roots., while a polynomial of degree `6` can have `6`, `4`, `2` or `0` Real roots.