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If $(x+a)$ is a factor of both the quadratic polynomials $x^{2}+p x+q$ and $x^{2}+L x+m$, where $p, q, l$ and $m$ are constants, then which one of the following is correct?
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The correct answer is:
$a=(m-q) /(l-p)(l \neq p)$
Given $(x+a)$ is a factor of quadratic polynomials $x^{2}+p x+q$ and $x^{2}+b x+m$
then $a^{2}-a p+q=0$
and $a^{2}-l a+m=0$
(i) $-($ ii $) \Rightarrow-a p+q+l a-m=0$
$\Rightarrow(I-p) a=m-q$
$\Rightarrow a=\frac{m-q}{l-p}(l \neq p)$
then $a^{2}-a p+q=0$
and $a^{2}-l a+m=0$
(i) $-($ ii $) \Rightarrow-a p+q+l a-m=0$
$\Rightarrow(I-p) a=m-q$
$\Rightarrow a=\frac{m-q}{l-p}(l \neq p)$
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