Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

Given:

taking LCM m^{2}x+ n^{2} = mn – 2mnx

On cross multiplying

m^{2}x+ 2mnx + n^{2} – mn = 0

Comparing with standard quadratic equation ax^{2} + bx + c = 0

a = m^{2}, b = 2mn, c = n^{2} – mn

Discriminant D = b^{2} – 4ac

= (2mn)^{2} – 4.m^{2}. (n^{2} – mn)

= 4m^{2}n^{2} – 4m^{2}n^{2} + 4m^{3}n > 0

Hence the roots of equation are real.

Roots α and β are given by

Hence the roots of equation are

24