Question

If $l,m,n$ are real, $l\ne m$, then the roots of the equation $(l-m)x^2-5(l+m)x-2(l-m)=0$, are

• A. real and unequal
• B. None of the above
• C. no solution
• D. real and equal

Answer 1

The correct option is D real and equal

Discriminant of the given equation is
$D=25(l+m{)}^2+8(l-m{)}^2\Rightarrow (l-m{)}^2>0(\because l\ne m),(l+m{)}^2\ge 0\therefore D>0$

Hence, the roots are real and unequal.