Q. 304.7( 3 Votes )

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

x2 – 4ax – b2 + 4a2 = 0

Answer :

Given: x2 – 4ax – b2 + 4a2 = 0

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


A = 1, B = – 4a, C = – b2 + 4a2


Discriminant D = B2 – 4AC


= (– 4a)2– 4.1. (– b2 + 4a2)


= 16a2 + 4b2 – 16a2 = 4 b2 > 0


Hence the roots of equation are real.



Roots are given by




x = (2a – b) or x = (2a + b)


Hence the roots of equation are (2a – b) or (2a + b)


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
Champ Quiz | Quadratic Equation48 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