Q. 224.3( 12 Votes )

If the roots of the equations ax2 + 2bx + c = 0 and are simultaneously real then prove that b2 = ac.

Answer :

Given the roots of the equations ax2 + 2bx + c = 0 are real.

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


A = a B = 2b C = c


Discriminant D1 = B2 – 4AC ≥ 0


= (2b)2 – 4.a.c ≥ 0


= 4(b2 –ac) ≥ 0


= (b2 –ac) ≥ 0 – – – – – (1)


For the equation


Discriminant D2 = b2 – 4ac ≥ 0


=


= 4(ac – b2) ≥0


= – 4(b2–ac) ≥0


= (b2 –ac) ≥0 – – – – – (2)


The roots of the are simultaneously real if (1) and (2) are true together


b2 –ac = 0


b2 = ac


Hence proved.


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