Question

If a + b + c = 0, a,b,c $ϵ$ Q, then the roots of the equation $(b+c-a)x^2+(c+a-b)x+(a+b-c)=0$ are :

• A. Rational
• B. Irrational
• C. Imaginary
• D. None

Answer 1

The correct option is A

Rational

Let A = b + c - a, B = c + a - b, C = a + b - c.

Then A+B+C = a + b + c = 0 and equation becomes

$A{x}^2$ + Bx + C = 0

$D=B^2-4AC=(C+A{)}^2-4AC=(C-A{)}^2$ .

Therefore, D is perfect square and A,B,C are rational numbers, therefore roots are rational.