Question

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

• A. irrational and different
• B. rational and different
• C. imaginary and different
• D. real and equal

Answer 1

Answer: (B)

rational and different

$(b+c)x^2-(a+b+c)x+a=0a,b,c\in qb+c\ne aD={(a+b+c)}^2-4\left(a\right)(b+c)=a^2+b^2+c^2-2ab-2ac+2bc={(a-b-c)}^{2}asb+c\ne a\therefore D>0$ always

$\therefore$ roots are rational and distinct as $D$ is a perfect square and greater than $0$