Q. If $p,q,r$ are real and $p \neq q$, then the roots of the equation $(p - q)x^{2} + 5(p + q)x - 2(p - q) = r$, are
A) Real and equal
B) Unequal and rational
C) Unequal and irrational
D) Nothing can be said
Explanation
(d)
Here, $a = (p - q),\ b = 5(p + q)$ and $c = - (2p - 2q + r)$
Now, $b^{2} - 4ac = 25(p + q)^{2} + 4(p - q)(2p - 2q + r)$
$= 25(p + q)^{2} + 8(p - q)^{2} + 4r(p - q)$
Hence, it depends on the value of $p,\ q$ and $r$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.