Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .
A)3 positive reals or 1 positive real; 1 negative real
B)3 positive reals or 1 positive real; no negative reals
C)no positive reals; no negative reals
D)1 positive real; 3 negative reals or 1 negative real
E)3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Question

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of  .
A)3 positive reals or 1 positive real; 1 negative real 
B)3 positive reals or 1 positive real; no negative reals 
C)no positive reals; no negative reals 
D)1 positive real; 3 negative reals or 1 negative real 
E)3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Quizplus · Accepted Answer

Using Descartes' Rule of Signs, we can determine the possible number of positive and negative real zeros by looking at the signs of the coefficients of the polynomial.
For the given polynomial 11eb80b1_b052_b96d_a291_773eb8e3273e_TB8633_11, we can see that there are no sign changes when we list the coefficients in descending order:
1 -8 24 -32 16 -5
This tells us that there could either be no positive real zeros or an even number of them. It also tells us that there could either be 3 negative real zeros or 1 negative real zero (since there are two sign changes when we look at the coefficients for the polynomial f(-x)).
Therefore, the best choice is B, which says that there are 3 possible positive real zeros or 1 possible positive real zero, and no negative real zeros.

Use Descartes' Rule of Signs to Determine the Possible Number