ALGEBRA 2, 2012
53

 PAGE: 396 SET: Exercises PROBLEM: 53

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 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 minus 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 impossible number of negative zeros of polynomial function is . Hence, by Descartessign 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 .

Therefore the number of negative zero is .

Option H is right choice.

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