Q. 314.7( 3 Votes )

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

4 x2 – 4a2x + (a4 – b4) = 0

Answer :

Given: 4x2 – 4a2x + (a4 – b4) = 0

Comparing with standard quadratic equation Ax2 + Bx + C = 0


A = 4, B = – 4a2, C = (a4 – b4)


Discriminant D = B2 – 4AC


= (– 4a2)2 – 4.4. (a4 – b4)


= 16a4 + 16b4 – 16a4 = 16 b4 > 0


Hence the roots of equation are real.



Roots are given by





Hence the roots of equation are


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