tell the maximum number of zeros

Question

Answer 1

Step 1:

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 7.

Step 2:

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

Descartes' rule states that the possible number of  positive zeros of polynomial function is the number of sign changes of the coefficients of or that number minus even number.

And the possible number of negative zeros of polynomial function is the number of sign changes of the coefficients of or that number minus even number.

.

Since there are  3 sign changes in the the possible number of  positive zeros of polynomial function is 3 or 1

Since there are  2 sign changes in the the possible number of  positive zeros of polynomial function is 2 or 0.

Solution:

The maximum number of real zeros of is 7.