If $\ell$, m, n are real,$\ell\ne m$, then the roots by the equation :$(\ell-m)x^2-5(\ell+m)x-2(\ell -m)=0$ are
(A)Real and equal
(B) Complex
(C)Real and Unequal
(D) None of these
My approach is as follow The discriminant $T = 25{\left( {\ell + m} \right)^2} + 8{\left( {\ell - m} \right)^2}$
$T = 33{\ell ^2} + 33{m^2} + 34\ell m$
$T = 33{\left( {\ell + m} \right)^2} - 32\ell m$
not able to approach from here
Your first $T$ i.e. $25{\left( {\ell + m} \right)^2} + 8{\left( {\ell - m} \right)^2}$ is always positive. So, the roots are real and unequal.