If a + b + c = 0,then the roots of the equati | vedclass

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(C) Given the quadratic equation $4ax^2 + 3bx + 2c = 0$.For the roots to be real,the discriminant $D = B^2 - 4AC$ must be $\ge 0$.Here,$A = 4a$,$B = 3

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Real

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(C) Given the quadratic equation $4ax^2 + 3bx + 2c = 0$.For the roots to be real,the discriminant $D = B^2 - 4AC$ must be $\ge 0$.Here,$A = 4a$,$B = 3b$,and $C = 2c$.$D = (3b)^2 - 4(4a)(2c) = 9b^2 - 32ac$.Given $a + b + c = 0$,we have $b = -(a + c)$.Substituting $b$ into the discriminant expression:$D = 9(-(a + c))^2 - 32ac = 9(a^2 + 2ac + c^2) - 32ac$.$D = 9a^2 + 18ac + 9c^2 - 32ac = 9a^2 - 14ac + 9c^2$.We can rewrite this as $D = 9(a^2 - \frac{14}{9}ac + c^2) = 9((a - \frac{7}{9}c)^2 + c^2(1 - \frac{49}{81})) = 9((a - \frac{7}{9}c)^2 + \frac{32}{81}c^2)$.Since $(a - \frac{7}{9}c)^2 \ge 0$ and $\frac{32}{81}c^2 \ge 0$,the discriminant $D$ is always $\ge 0$.Therefore,the roots are real.

If $a + b + c = 0$,then the roots of the equation $4ax^2 + 3bx + 2c = 0$ are

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