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

Feb 13, 2016

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.