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.