First slide

Theory of equations

Question

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

Moderate

A

Rational
B

Non-real
C

Irrational
D

Equal

Solution

Here $(b + c - 2 a) + (c + a - 2 b) + (a + b - 2 c) = 0$
Therefore the roots are rational

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