Question

For any numbers a and b and an even natural number n, show that the following equation has at most two solutions:

Answer 1

\[x^{n}+ax+b=0\]

Answer 2

Can't u just say that If you differentiate this twice you are just left with a power of x (always positive so local minimum) so the most that the curve can cross the x-axis is twice?

Answer 3

I have to prove it mathematically, but I figured it out. You essentially use Rolles Theorem and prove by contradiction that there can't exist more than two roots.

Answer 4

Horses for courses.....