True or False: A polynomial of degree 3 with real coefficients mist have two nonreal zeroes.

Question

jim_thompson5910 · Answer

Can a cubic equation have 3 x intercepts?

anonymous · Answer

Why couldn't it? I don't understand why there has to  be nonreal

jim_thompson5910 · Answer

you're correct, it can have 3 x-intercepts, so it's false

anonymous · Answer

Ok thanks! Would any other degree absolutely have to have nonreal?

jim_thompson5910 · Answer

No there is no rule that says any degree polynomial has a certain number of nonreal roots. It depends on what the actual polynomial is.

anonymous · Answer

No. The only rule you can give the number of non-real zeros is the fact that they come in pairs. That is, it's impossible for any polynomial to have an odd number of nonreal zeros.

anonymous · Answer

Why does the question mention real coefficents?

anonymous · Answer

For example, a degree 5 polynomial could have the following combinations:
5 real
3 real, 2 nonreal
1 real, 4 nonreal

anonymous · Answer

Thanks that makes sense! And does the real coefficients have nothing to do with it at all? Why was it mentioned

anonymous · Answer

It's mentioned because you're dealing with the complex conjugate root theorem, which is only a statement about polynomials with real coefficients. Polynomials with non-real coefficients are a totally different can of worms, and you probably won't even dip into that can one bit, so don't worry too much about it.

anonymous · Answer

Good questions =) Keep it up.

anonymous · Answer

And complex conjugate zeroes only apply if the coefficients are real then?