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Q.

$I f e q u a t i o n a x^{2} + b x + c = 0 (a, b, c \in R, a \neq 0) a n d 2 x^{2} + 3 x + 4 = 0 h a v e a c o m m o n r o o t, t h e n a : b : c e q u a l s :$

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a

2:3:4

b

1:2:3

c

4:2:3

d

3:2:1

answer is A.

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Detailed Solution

$\begin{array}{l} G i v e n E q u a t i o n 2 x^{2} + 3 x + 4 = 0 \\ Δ = b^{2} - 4 a c = 9 - 4 (2) 4 \Rightarrow 9 - 32 \Rightarrow - 23 < 0 \\ ∴ T h e E q u a t i o n 2 x^{2} + 3 x + 4 = 0 h a v e c o m p e x r o o t s \\ I f a x^{2} + b x + c = 0 a n d 2 x^{2} + 3 x + 4 = 0 h a v e c o m m o n r o o t s t h e n \\ a x^{2} + b x + c = 0 a l s o h a v e c o m p l e x r o o t s \\ I t w i l l b e o b t a i n e d a t a = 2, b = 3, c = 4 \\ ∴ a : b : c = 2 : 3 : 4 \end{array}$

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