Question

If $a,b,c\in R$ and $a\ne b$, then both the roots of the equation $2(a-b)x^2-11(a+b+c)x-3(a-b)=0$ are always

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

Answer 1

The correct option is B real and unequal

$2(a-b)x^2-11(a+b+c)x-3(a-b)=0$

$\Delta =b^2-4ac=121(a+b+c{)}^2+24(a-b{)}^2>0[\because a\ne b]$

$\Rightarrow$ Roots are real and unequal.