5
$\begingroup$

Given that the following equation $$p(x)=a_0x^n+a_1x^{n-1}+...+a_{n-1}x+a_n=0$$ has $n$ distinct real roots. Prove that $$\frac{n-1}{n}>\frac{2a_0a_2}{a_1^2}$$

  • 0
    You need to add that $n$ distinct real roots. (For $n=2$, this gives the condition $a_1^2 > 4a_0 a_2$)2012-10-21
  • 0
    Yes, real roots, sorry2012-10-21
  • 0
    Woah, neat. I would have thought you could find $a_i$ that break this condition, but they all give polynomials with nondistinct or nonreal roots!2012-10-21

2 Answers 2