Q. 364.5( 8 Votes )

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

12abx2 – (9a2 – 8b2)x – 6ab = 0, where a ≠ 0 and b ≠ 0

Answer :

Given: 12abx2 – (9a2 – 8b2)x – 6ab = 0

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


A = 12ab, B = – (9a2 – 8b2), C = – 6ab


Discriminant D = B2 – 4AC


= [ – (9a2 – 8b2)]2 – 4.12ab. – 6ab


= 81a4 – 144a2b2 + 64b4 + 288 a2b2


= 81a4 + 144a2b2 + 64b4


= (9a2 + 8b2)2 > 0 Using a2 + 2ab + b2 = (a + b)2


Hence the roots of equation are real.



= 9a2 + 8b2


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
Get To Know About Quadratic Formula42 mins
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 EquationsFREE Class
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Quadratic Equation: Previous Year NTSE Questions32 mins
Champ Quiz | Quadratic Equation33 mins
Balance the Chemical Equations49 mins
Champ Quiz | Quadratic Equation48 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