Q. 164.5( 12 Votes )

By using the method of completing the square, show that the equation 2x2 + x + 4 = 0 has no real roots.

Answer :

2x2 + x + 4 = 0

4x2 + 2x + 8 = 0 (multiplying both sides by 2)


4x2 + 2x = - 8


[Adding on both sides]


using a2 + 2ab + b2 = (a + b)2


But cannot be negative for any real value of x


So there is no real value of x satisfying the given equation.


Hence the given equation has no real roots.


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