# 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

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic Equations51 mins
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Quadratic Equation: Previous Year NTSE Questions32 mins
Champ Quiz | Quadratic Equation33 mins
Understand The Concept of Quadratic Equation45 mins
Balance the Chemical Equations49 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses