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

a^{2}b^{2}x^{2} – (4b^{4} – 3a^{4})x – 12a^{2}b^{2} = 0, a ≠ 0 and b ≠ 0

Given: a^{2}b^{2}x^{2} – (4b^{4} – 3a^{4})x – 12a^{2}b^{2} = 0

Comparing with standard quadratic equation Ax^{2} + Bx + C = 0

A = a^{2}b^{2}, B = – (4b^{4} – 3a^{4}), C = – 12a^{2}b^{2}

Discriminant D = B^{2} – 4AC

= [ – (4b^{4} – 3a^{4})]^{2} – 4a^{2}b^{2}. – 12a^{2}b^{2}

= 16b^{8} – 24a^{4}b^{4} + 9a^{8} + 48 a^{4}b^{4}

= 16b^{8} + 24a^{4}b^{4} + 9a^{8}

= (4b^{4} + 3a^{4})^{2} > 0 Using a^{2} + 2ab + b^{2} = (a + b)^{2}

Hence the roots of equation are real.

=

Roots are given by

Hence the roots of equation are

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