Question

The roots of the quadratic equation $(a+b)x^2-3bx-3a=0\forall a,b\in R$ are

• A. real and distinct.
• B. imaginary.
• C. real and equal
• D. none of these

Answer 1

The correct option is A real and distinct.

$(a+b)x^2-3bx-3a=0$
For the given equation to be quadractic,
$a+b\ne 0\cdots \left(1\right)$
Now,
$D=9b^2+12a(a+b)=9b^2+12a^2+12ab=6(a^2+2ab+b^2)+6a^2+3b^2=6(a+b{)}^2+6a^2+3b^2$
$\Rightarrow D>0(\because a+b\ne 0)$
So, roots are real and distinct.