What are the possible numbers of positive real, negative real, and complex zeros of f(x) = -7x4 - 12x3 + 9x2 - 17x + 33

Question

fionacndg · Answer

A. Positive Real: 3 or 1
    Negative Real: 1
    Complex: 2 or 0
	
B. Positive Real: 3 or 1
    Negative Real: 2 or 0
    Complex: 1
	
C. Positive Real: 1
    Negative Real: 3 or 1
    Complex: 2 or 0

D. Positive Real: 4, 2 or 0
    Negative Real: 1
    Complex: 0 or 1 or 3

parthkohli · Answer

Do you know Descartes' Rule of Signs?

fionacndg · Answer

A little bit.

parthkohli · Answer

Well, use it.

fionacndg · Answer

yep still confused.

fionacndg · Answer

would the positive real be 3 or 1??

hartnn · Answer

thats correct :)
and since the co-efficients are real,
the number of complex zeros should be even 
(as complex zeros occur in pair if co-efficients are real)

hartnn · Answer

ask if any more doubts :)

fionacndg · Answer

Okay! super I am getting somewhere!

fionacndg · Answer

so the complex zeros are 2 or zero?

hartnn · Answer

yes :)

fionacndg · Answer

thank you so much for helping! I really just needed some verification!

hartnn · Answer

most welcome ^_^

fionacndg · Answer

for anyone later viewing, the answer is A