If (x + a) is a factor of $x^{2} + p x + q$ and $x^{2} + m x + n$ then the value of a is

\frac{m - p}{n - q}

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\frac{n - q}{m - p}

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\frac{n + q}{m + p}

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\frac{m + p}{n + q}

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Solution

The correct option is B $\frac{n - q}{m - p}$
Putting - a in anyone of them will yuld 0.
$a^{2} - a p + q = 0$
$a^{2} = a p - q$
$a^{2} - a m + n = 0$
$a^{2} = a m - n$
$a p - q = a m - n$
$a p - q = a m - n$
$a p - a m = q - n$
$a (p - m) = q - n \Rightarrow a = \frac{q - n}{p - m} = \frac{n - q}{m - p}$

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