Question

If a is real, what is the only real number that could be a miltiple root of x^3+ax+1=0

Answer 1

Maybe think about it like a quadratic equation? \[
x(x^2)+a(x) + 1=0
\]

Answer 2

I dunno, I'm grasping at straws.

Answer 3

i tried that but didn't have much luck! the whole "real" thing in the question doesn't seem much of a help

Answer 4

what does that mean
"the only real number that could be a multiple root of ..."

Answer 5

like a root with multiplicity 2?

Answer 6

or even multiplicity 3

Answer 7

i wrote the whole question as it was, maybe they mean like \[\pm2\]

Answer 8

say x=k is a zero (with multiplicty 2)
f(k)=0
that is k^3+ak+1=0
so if we see what (x^3+ax+1)/(x-k) is we get