Let α > β be the two distinct roots of some Adfected quadratic equation ax² + bx + c = 0 with c ≠ 0 , Prove that there exists unique m & n such that α ∈ \lbrack m , n \rbrack and m , n being integers satisfy the quadratic equation simul†an eously i.e, am² + bn + c = 0 and an² + bm + c = 0 .

Let α > β be the two distinct roots of some Adfected quadratic equat

1.	Let α > β be the two distinct roots of some Adfected quadratic equation ax² + bx + c = 0 with c ≠ 0 , Prove that there exists unique m & n such that α ∈ \lbrack m , n \rbrack and m , n being integers satisfy the quadratic equation simul†an eously i.e, am² + bn + c = 0 and an² + bm + c = 0 .
Answer» Let α > β be the two distinct roots of some Adfected quadratic equation ax² + bx + c = 0 with c ≠ 0 , Prove that there exists unique m & n such that α ∈ \lbrack m , n \rbrack and m , n being integers satisfy the quadratic equation simul†an eously i.e, am² + bn + c = 0 and an² + bm + c = 0 .