So I have to show 2 things.

i) If:

has 2 real roots (say x1 and x2), then show (in C) that x3 is also a real root.Code:p(x)=x^3+ax^2+bx+c

I know from intuition this is obvious , since a cubed function that hits the x axis twice MUST go back in the other direction, but Im having troubling proving it. I have tried a couple things with no success.

Thoughts, I know that P(x)=(x-x1)(x-x2)(x-x3) but that leads me no where, and I also know that:

-a=x1+x2+x3

b=x1x2+x1x3+x2x3

-c=x1x2x3

ii) is giving me more problems. it asks to give a formula for x3 in terms of x1 and x2.

Any help or guidance is much appreciates.

Thanks