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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.
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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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