any ideas?

Bexultan wrote: Define a quadratic trinomial to be "good", if it has two distinct real roots and all of its coefficients are distinct. Do there exist 10 positive integers such that there exist 500 good quadratic trinomials coefficients of which are among these numbers? There are $\binom{10}3=120$ triplets $a>b>c$ possible amongst the ten positive integers. And since $c^2<4ab$, there are at most four good quadratics with these numbers : $ax^2+bx+c$, $cx^2+bx+a$, $bx^2+ax+c$ and $cx^2+ax+b$ And so $\boxed{\text{At most }480\text{ good quadratics}}$