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Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
36x2 – 12ax + (a2 – b2) = 0
Given: 36x2 – 12ax + (a2 – b2) = 0
Comparing with standard quadratic equation Ax2 + Bx + C = 0
A = 36, B = – 12a, C = a2 – b2
Discriminant D = B2 – 4AC
= (– 12a)2 – 4.36.(a2 – b2)
= 144a2 – 144a2 + 144 b2 = 144 b2 > 0
Hence the roots of equation are real.
Roots are given by
Hence the roots of equation are