Q. 354.1( 10 Votes )

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

a2b2x2 – (4b4 – 3a4)x – 12a2b2 = 0, a ≠ 0 and b ≠ 0

Answer :

Given: a2b2x2 – (4b4 – 3a4)x – 12a2b2 = 0

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


A = a2b2, B = – (4b4 – 3a4), C = – 12a2b2


Discriminant D = B2 – 4AC


= [ – (4b4 – 3a4)]2 – 4a2b2. – 12a2b2


= 16b8 – 24a4b4 + 9a8 + 48 a4b4


= 16b8 + 24a4b4 + 9a8


= (4b4 + 3a4)2 > 0 Using a2 + 2ab + b2 = (a + b)2


Hence the roots of equation are real.



=


Roots are given by





Hence the roots of equation are


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