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Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
taking LCM m2x+ n2 = mn – 2mnx
On cross multiplying
m2x+ 2mnx + n2 – mn = 0
Comparing with standard quadratic equation ax2 + bx + c = 0
a = m2, b = 2mn, c = n2 – mn
Discriminant D = b2 – 4ac
= (2mn)2 – 4.m2. (n2 – mn)
= 4m2n2 – 4m2n2 + 4m3n > 0
Hence the roots of equation are real.
Roots α and β are given by
Hence the roots of equation are