Question

If $p,q,r$ are real and $p\ne q,$ then roots of the equation $(p-q)x^2+5(p+q)x-2(p-q)=0$ are

• A. Real and equal
• B. Complex
• C. Real and unequal
• D. None of these

Answer 1

Answer: (C)

Real and unequal

Discriminant $=b^2-4ac$
$=25(p+q{)}^2+8(p-q{)}^2$
Hence, $D\ge 0$
Hence, roots are real.
Also $p$ and $q$ are real.
$\therefore D\ne 0$
Hence, roots are not equal.