Question

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

• A. complex
• B. real and equal
• C. real and unequal
• D. none of these

Answer 1

Answer: (C)

real and unequal

$l,m,n\in Rl\ne m(l-m)x^2-5(l+m)x-2(l-m)=0D={(-5(l+m\left)\right)}^2+8{(l-m)}^2$

As ${(l+m)}^2$ and ${(l-m)}^2$ both greater than zero as $l\ne m$ so $D$ greater than zero so roots are real and distinct.