# Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2 – (2b – 1)x + (b2 – b – 20) = 0

Given: x2 – (2b – 1)x + (b2 – b – 20) = 0

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

A = 1, B = – (2b – 1), C = (b2 – b – 20)

Discriminant D = B2 – 4AC

= [ – (2b – 1)2] – 4.1. (b2 – b – 20) Using a2 – 2ab + b2 = (a – b)2

= 4b2 – 4b + 1 – 4b2 + 4b + 80 = 81 > 0

Hence the roots of equation are real.

Roots are given by

x = (b + 4) or x = (b – 5)

Hence the roots of equation are (b + 4) or (b – 5)

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 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