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

Rational

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Irrational

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Integers

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Complex

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D Rational
Put $A = b + c - 2 a$
$B = c + a - 2 b$
$C = a + b - 2 c$
$∴ A + B + C = 0$
So equation can be written as $A x^{2} + B x + C = 0$ where $A + B + C = 0$ Since $A + B + C = 0$
$∴$ Roots are $1 o r \frac{C}{A}$
$∴$ Roots are rational

Suggest Corrections

Similar questions

If a, b, c belongs to Q then roots of the equation (b+c-2a)x²+(c+a-2b)x+(a+b-2c)=0 are

a)rational b) non real c) irrational d) equal

a x^{2} + b x + c = 0

a \neq b \neq c

a x^{2} + 2 b x + c = 0

a, b, c \in R^{+}

2 b = a + c

a x^{2} + 2 b x + c = 0

a, b, c

a x^{2} + 2 b x + c = 0

Join BYJU'S Learning Program