The polynomial function is .

The maximum number of real zeros of a polynomial function is equal to the degree of that polynomial function.

So the maximum number of real zeros of is .

Descartes rule of signs is useful for finding the maximum number of real zeros of the polynomial function.

Descartes sign rule :

The possible number of positive zeros of polynomial function is the number of sign changes of the coefficients of or that number positive even number.

.

Since there are sign changes in the the possible number of positive zeros of polynomial function is .

Since there are sign changes in the the possible number of negative zeros of polynomial function is .

Hence, by Descartes sign rule, the maximum number of zeros is .

Make a table of a possible combinations of real and imaginary zeros.

Number of postive real zeros	negative zeros	imaginary zeros	Total number of zeros

  \ \

The maximum number of real zeros of is . \ \