Q. 114.3( 21 Votes )

If ad <span lang=

Answer :

We know, that roots of a quadratic equation in general form


Ax2 + Bx + C = 0


if and only if D ≥ 0


Where, D = B2 - 4AC


In given equation,


A = a2 + b2


B = 2(ac + bd)


C = c2 + d2


D = (2ac + 2bd)2 - 4(a2 + b2)(c2 + d2)


D = 4a2c2 + 4b2d2 + 8abcd - 4(a2c2 + a2d2 + b2c2 + b2d2)


D = 4a2c2 + 4b2d2 + 8abcd - 4a2c2 - 4a2d2 - 4b2c2 - 4b2d2


D = 8abcd - 4b2c2 - 4a2d2


D = - 4(b2c2 + a2d2 + 2abcd)


D = - 4(bc + ad)2


Now, square of any number is always greater than zero,


(bc + ad)2 > 0 [As ad ≠ bc , (bc + ad)2 ≠ 0 ]


- 4(bc + ad)2 < 0


D < 0


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
All GrammarAll GrammarAll Grammar41 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