Q. 285.0( 1 Vote )

Find the values of p for which the quadratic equation:

(2p + 1)x2 – (7p + 2)x + (7p – 3) = 0 have equal roots.

Answer :

(2p + 1)x2 – (7p + 2)x + (7p – 3) = 0


Let us find Discriminant of the given equation. For equal roots of a quadratic equation, Discriminant equals to zero.


Discriminant, D = b2 – 4 ac


Where, a = (2 p + 1), b = (7 p + 2) and c = (7 p – 3)


Putting these values for finding discriminant.


D = (7 p + 2)2 – 4 (2 p + 1) ( 7 p – 3)


D = 49 p2 + 28 p + 4 – (56 p2 + 4 p – 12)


Now for equal roots D = 0


49 p2 + 28 p + 4 – (56 p2 + 4 p – 12) = 0


–7 p2 + 24 p + 16 = 0


7 p2 – 24 p – 16 = 0


For finding values of “p”, apply the Quadratic formula,


We know that the solution of equation ax2 + bx + c = 0 is given by:



For our quadratic equation, a = 7, b = – 24 and c = – 16





So, p = –56/14 or p = 8/14


Thus the possible values of p are – 4 and 4/7


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 FormulaGet To Know About Quadratic FormulaGet To Know About Quadratic Formula42 mins
Quiz | Knowing the Nature of RootsQuiz | Knowing the Nature of RootsQuiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphsTake a Dip Into Quadratic graphsTake a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for FoundationFoundation | Practice Important Questions for FoundationFoundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic EquationsNature of Roots of Quadratic EquationsNature of Roots of Quadratic Equations51 mins
Getting Familiar with Nature of Roots of Quadratic EquationsGetting Familiar with Nature of Roots of Quadratic EquationsGetting Familiar with Nature of Roots of Quadratic Equations51 mins
Quadratic Equation: Previous Year NTSE QuestionsQuadratic Equation: Previous Year NTSE QuestionsQuadratic Equation: Previous Year NTSE Questions32 mins
Understand The Concept of Quadratic EquationUnderstand The Concept of Quadratic EquationUnderstand The Concept of Quadratic Equation45 mins
Balance the Chemical EquationsBalance the Chemical EquationsBalance the Chemical Equations49 mins
Champ Quiz | Quadratic EquationChamp Quiz | Quadratic EquationChamp Quiz | Quadratic Equation33 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
caricature
view all courses