If $(x + k)$ is a common factor of the expressions $x^{2} + p x + q$ and $x^{2} + l x + m$ , then $k$ is equal to

\frac{p - q}{l + m}

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

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

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

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Solution

The correct option is D $\frac{q - m}{p - l}$
$(x + k)$ is a common factor of the expression
$x^{2} + p x + q$ and $x^{2} + l x + m$
$x^{2} + p x + q = 0$ $x^{2} + l x + m = 0$
$x = - k$ $x = - k$
$k^{2} - k p + q = 0$ $k^{2} - l k + m = 0$
$\frac{k^{2} - l k \pm m = 0}{(l - o) k + (q - m) = 0}$
$k = \frac{q - m}{p - l}$

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Similar questions

If the ratio of the roots of the equation $x^{2}$ +px+q=0 be equal to the ratio of the roots of $x^{2}$ +lx+m=0. Then

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If x + a is a common factor of expressions $f (x) = x^{2} + p x + q a n d g (x) = x^{2} + m x + n;$ show that : $a = \frac{n - q}{m - p}$

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(x^{2} + p x + q)

(x^{2} + l x + m)

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