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Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
4 x2 + 4bx – (a2 – b2) = 0
Given: 4x2 + 4bx – (a2 – b2) = 0
Comparing with standard quadratic equation Ax2 + Bx + C = 0
A = 4, B = 4b, C = – (a2 – b2)
Discriminant D = B2 – 4AC
= (4b)2 – 4.4. – (a2 – b2)
= 16b2 + 16a2 – 16b2 = 16 a2 > 0
Hence the roots of equation are real.
Roots are given by
Hence the roots of equation are