Question

The roots of the equation $(b+c)x^2-(a+b+c)x+a=0$, where $a,b,c\in Q$ and $b+c\ne a$, are

• A. rational and equal
• B. rational and distinct
• C. irrational and equal
• D. cannot be determined

Answer 1

The correct option is B rational and distinct

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

$\Delta =(a+b+c{)}^2-4(b+c)a$
$=a^2+b^2+c^2+2ab+2bc+2ca-4ab-4ac$
$=a^2+b^2+c^2-2ab+2bc-2ac$
$=(a-b-c{)}^2>0$ as $b+c\ne a$

$\Delta$ is a perfect square and positive.

Hence, the roots are rational and distinct.