Let $\alpha > \beta$ be the two distinct roots of some quadratic equation $ax² + bx + c = 0$ with $a , b, c ≠ 0$ , Prove that there exists unique $m$ & $n$ such that $\alpha\in[ m , n ]$
and $m$ , $n$ being integers satisfy the quadratic equation simultaneously i.e, $am² + bn + c = 0$ and $an² + bm + c = 0$ .
Another request- Please let me know the graphical interpretation of this question profile .