Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .
A) no positive reals; no negative reals
B) 1 positive real; 3 negative reals or 1 negative real
C) 0 positive real; 3 negative reals or 1 negative real
D) 3 positive reals or 1 positive real; no negative reals
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) no positive reals; no negative reals 
B) 1 positive real; 3 negative reals or 1 negative real 
C) 0 positive real; 3 negative reals or 1 negative real 
D) 3 positive reals or 1 positive real; no negative reals 
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Quizplus · Accepted Answer

- Count the sign changes in the coefficients of the polynomial.
11eb11e8_19ca_111f_ad38_851cd4dd3571_TB4588_11: no sign change
- If there are any sign changes, subtract multiples of 2 for each sign change from the number of sign changes.
Therefore, there are 0 positive real zeros.
- Next, substitute -x for x and count the sign changes in the coefficients of the resulting polynomial.
11eb11e8_19ca_111f_ad38_851cd4dd3571_TB4588_11(-x): 3 sign changes
- Subtract multiples of 2 for each sign change from the number of sign changes.
Therefore, there are 3 negative real zeros or 1 negative real zero.

Thus, the correct choice is C.

Use Descartes' Rule of Signs to Determine the Possible Number