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| 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 |
|
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The maximum number of real zeros of is 
.
Therefore the number of negative zero is .
Option H is right choice.
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Simply chose a support option
  
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