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If $a + b + c = 0$ , the straight line $2 a x + 3 b y + 4 c = 0$ passes through the fixed point $(α, β)$ then $α + 3 β =$

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Detailed Solution

$4 a + 4 b + 4 c = 0, 2 a x + 3 b y + 4 c = 0$

$\frac{2 x}{4} = \frac{3 y}{4} = 1 \Rightarrow (α, β) = (2, \frac{4}{3}) \Rightarrow α + 3 β = 2 + 4 = 6$

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