If the roots of the equation $ax^2 + 2bx + c=0$ are real and disrinct, then show that the roots of the equation $x^2-2(a+b)x+a^2+b^2+2c^2=0$ are non-real complex numbers.
For the first equation discriminant >0, which gives $b^2-ac>0$.
for the second equation we have to show that discriminant <0. that is where I am facing problem.
$\Delta = 4(a+b)^2-4(a^2+b^2+2c^2)= 8(ab-c^2)$