If a + b + c = 0, the correct statements for the equation $a x^{2} + b x + c = 0$ are

One of the roots is +ve

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$\frac{(a + b)}{a}$ is a root of the equation

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$\frac{c}{a}$ is a root of the equation.

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$\frac{- (a + b)}{a}$ is a root of the equation

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Solution

The correct option is D
$\frac{- (a + b)}{a}$ is a root of the equation

If we substitute 1 in the equation, we get a+b+c = 0
$\Rightarrow$ 1 is a root of the equation $\Rightarrow$ Option A

Let the other root be $α$

$α$ x 1 = $\frac{c}{a}$
$α$ = $\frac{c}{a}$ $\Rightarrow O p t i o n A, B$
$α$ + 1 = $\frac{- b}{a}$
$α$ = $\frac{- b}{a} - 1$

$= \frac{- b - a}{a}$
$= \frac{- (b + a)}{a} \Rightarrow O p t i o n C$

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If a + b + c = 0, the correct statements for the equation ax2+bx+c=0 are

The correct option is D −(a+b)a is a root of the equation If we substitute 1 in the equation, we get a+b+c = 0 ⇒ 1 is a root of the equation ⇒ Option A Let the other root be α α x 1 = ca α = ca ⇒OptionA,B α + 1 = −ba α = −ba−1 =−b−aa =−(b+a)a⇒OptionC

If a + b + c = 0, the correct statements for the equation $a x^{2} + b x + c = 0$ are