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If (x-2) is a common factor of the expressions $x^{2} + ax + b$ and $x^{2} + cx + d$ , then $\frac{b - d}{c - a} =$

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Detailed Solution

$∴ x = 2 is a root of x^{2} + ax + b = 0 and x^{2} + cx + d = 0$

$∴ 4 + 2 a + b = 0, 4 + 2 c + d = 0$

$\Rightarrow 2 a + b = 2 c + d$

$\Rightarrow \frac{b - d}{c - a} = 2$

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