Question

Could someone help me prove that irrational roots occur in pairs? (Part of the conjugate roots theorem)

Answer 1

I'm stuck :-/

Answer 2

Remember how when you were solving quadratic equations and there were some equations that you could factor and some that you couldn't?

Answer 3

yeah...

Answer 4

Well, either you could factor it or you couldn't.
The ones that you could factor, you could factor because both of their roots were rational. The ones you couldn't, were because both roots were irrational.

Answer 5

do i assume my equation has an even degree?

Answer 6

well not exactly, you could factor an equation like
f(x)=(x+sqrt(2))(x-sqrt(2))

Answer 7

You could, but not by the "normal" methods of factoring.

Answer 8

I need another hint please :-)

Answer 9

Well....thinking....

Answer 10

Say you have an equation.
If it's of even degree, then it involves roots. But the roots can be positive or negative, without changing the value under the radical. (I don't think that makes any sense...if you don't understand, ask me to explain it again.)
If it's of odd degree, then you can just factor one solution out and it becomes an equation of even degree.
Does that make any sense?

Answer 11

ohhhhh got it thank you Nory :-)

Answer 12

You're welcome. :) A star for you *

Answer 13

merci!