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If 2 is a root of $a x^{2} + b x + c = 0$ then the point of concurrence of the lines $a x + 2 b y + 3 c = 0$ is

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$(12, 3)$

$(4, 2)$

$(1, 2)$

$(2, 3)$

answer is A.

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Detailed Solution

2 is a root of $a x^{2} + b x + c = 0$
$4 a + 2 b + c = 0 a n d a x + 2 b y + 3 c = 0$
$c = - 4 a - 2 b \Rightarrow a x + 2 b y - 3 (4 a - 2 b) = 0$
$a (x - 12) + 2 b (y - 3) = 0$
The point of concurrence of the lines is (12, 3)

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