Question

Find the complex zeros of f(x) = x^6 + x^5+ x^4 + 4x^3 – 12x^2 + 12

Answer 1

i think it's 6, 4, 2 or 0

Answer 2

hmm...can you make sure there isnt a term missing? inbetween the -12x^2 and 12? otherwise, this is not something that could be done by hand most likely. You would need either a calculator or computer.

Answer 3

there's no term missing, in between the -12x^2 and 12 is +

Answer 4

hm...well, none of those numbers you posted are zeros. If you want to check if a number is a zero of a polynomial, plug in the number and make sure you get 0 for an answer. For example, if I thought 0 was a zero of the polynomial, I would compute:\[0^6+0^5+0^4+4\cdot0^3-12\cdot 0^2+12\]which gives me an answer of 12. Not 0. Likewise, if you plug in any of the other numbers you guessed, none of them would work either.

Answer 5

hmm.. try the descartes' rule of signs

Answer 6

im not quite sure though, just checking my answer, and my answer is the possible complex zeros are 6, 4, 2 or 0

Answer 7

oh, was the question, "what are the possible roots?" or "what are the roots?"

Answer 8

possible roots, yeah sorry i forgot to type that in

Answer 9

lol <.< thats totally different then. Yes you are correct. You forgot 1 and 12 though. and take off 0. You have to use the Rational Roots Theorem.