Let $P(x)=x^4+ax^3+bx+c$, $a,b,c$ are real, and all the roots of the polynomial are different. Prove that $ab<0$. I have tried connecting the $a,b,c$ written in Viet's, and pulling something out of that, all I got is that if all the roots of the polynomial are real and $c>0$ that the inequality stands.
Asked
Active
Viewed 99 times
