hey all,
i got the following problem to solve:
i got this term: 27*g^2+4*p^3<0
and i need to proof that there are three real roots to this function:
x^3+px+q=0
is it enough to solve it by min/max points of the function?
Hello danneeI'm sure you mean:Then the proof goes like this:
Every cubic has at least one real root, so let's assume that has a real root . Then:, for some constants and .Comparing coefficients:
So:
This can be expanded and factorised to give:
has two real roots, and hence has three real roots.
Grandad