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

1 Answer
Feb 13, 2016

Answer:

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.