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 positive odd 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 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 |
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The maximum number of real zeros of is
.