If the equations x2 + ax + b = 0 and x2 + px + q = 0 have a common root, then that root is

b − q p − a or aq − bp b − q

b − q p − a or aq − bp b − q

b − q p − q or a − b p − q

b + q p + a or ab − bp p − q

b + q p − a or aq − bp p − a

b − q p − a or aq − bp b − q

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If the equations x² + ax + b = 0 and x² + px + q = 0 have a common root, then that root is

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$\frac{b - q}{p - q} or \frac{a - b}{p - q}$

$\frac{b + q}{p + a} or \frac{ab - bp}{p - q}$

$\frac{b + q}{p - a} or \frac{aq - bp}{p - a}$

$\frac{b - q}{p - a} or \frac{aq - bp}{b - q}$

answer is D.

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Subtracting one from another $(a - p) x + b - q = 0$

$\Rightarrow x = \frac{b - q}{p - a}$

$\frac{x^{2}}{aq - bp} = \frac{x}{b - q} = \frac{1}{p - a}$

$\Rightarrow If x \neq 0 \Rightarrow \frac{x}{aq - bp} = \frac{1}{b - q} \Rightarrow x = \frac{aq - bp}{b - q}$

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