State how many imaginary and real zeros the function has.

f(x) = x4 + 12 x3 + 37x2 + 12x + 36

Question

State how many imaginary and real zeros the function has.

f(x) = x4 + 12 x3 + 37x2 + 12x + 36

tkhunny · Answer

No positive Real zeros.  Do you know why?

anonymous · Answer

no I don't

tkhunny · Answer

Have you met Descartes' Rule of Signs.

anonymous · Answer

oh yes I remember now

zzr0ck3r · Answer

wow im glad you came....I was about to suggest Tartaglia's method for solving 4th degree polynomials...

tkhunny · Answer

Okay, how about negative Real Zeros.

anonymous · Answer

well doesn't it say that no matter how many solutions their is whether its positive or negative it shows you the degree of the polynomial, or two less, or four less, or....

tkhunny · Answer

No, that is a different theorem.

f(-x) = x4 - 12 x3 + 37x2 - 12x + 36

Four sign changes.  There are Four, Two, or Zero Negative Real solutions.  Had there been any positive ones, this would have been less clear.

anonymous · Answer

oh I see. now I understand