First slide

Theory of equations

Question

If $a + b + c = 0, a \neq 0, a, b, c \in Q$ , then both the roots of the equation ${ax}^{2} + bx + c = 0$ are

Moderate

A

Rational
B

Non-real
C

Irrational
D

Zero

Solution

$D = b^{2} - 4 ac = {(- a - c)}^{2} - 4 ac (∵ a + b + c = 0)$
$= {(a + c)}^{2} - 4 ac = {(a - c)}^{2} \geq 0$
Hence roots are rational.

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