If a + b + c = 0,a neq 0,a, b, c in Q,then bo | vedclass

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(A) Given the quadratic equation $ax^2 + bx + c = 0$ where $a, b, c \in Q$ and $a + b + c = 0$.
Since $a + b + c = 0$,we have $b = -(a + c)$.
The di

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(A) Given the quadratic equation $ax^2 + bx + c = 0$ where $a, b, c \in Q$ and $a + b + c = 0$.
Since $a + b + c = 0$,we have $b = -(a + c)$.
The discriminant $D$ of the quadratic equation is given by $D = b^2 - 4ac$.
Substituting $b = -(a + c)$,we get $D = (-(a + c))^2 - 4ac = (a + c)^2 - 4ac$.
Expanding this,$D = a^2 + 2ac + c^2 - 4ac = a^2 - 2ac + c^2 = (a - c)^2$.
Since $a, c \in Q$,$(a - c)^2$ is a perfect square of a rational number,which is always $\ge 0$.
Since the discriminant $D$ is a perfect square of a rational number,the roots are given by $x = \frac{-b \pm \sqrt{D}}{2a} = \frac{a + c \pm (a - c)}{2a}$.
This results in $x_1 = \frac{2a}{2a} = 1$ and $x_2 = \frac{2c}{2a} = \frac{c}{a}$.
Since $a, c \in Q$ and $a 
eq 0$,both roots are rational numbers.

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

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