a + b + c = 0 then the roots of the equation $4 a x^{2} + 3 b x + 2 c = 0$ where $a, b, c \in R$

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can-not be decided

real and distinct

real and equal

imaginary

answer is A.

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Detailed Solution

Discriminant =
$\begin{array}{l} 9 b^{2} - 32 a c \\ = 9 {(a + c)}^{2} - 32 a c \\ = 9 a^{2} - 14 a c + 9 c^{2} \\ = \frac{c^{2}}{36} [{(18 \frac{a}{c} - 14)}^{2} + 138] > 0 \end{array}$

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