A) \[l+p\]
B) \[m-q\]
C) \[\frac{l-p}{m-q}\]
D) \[\frac{m-q}{l-p}\]
Correct Answer: D
Solution :
Since \[(x+k)\]is a common factor of \[f(x)={{x}^{2}}+px+q\]and \[g(x)={{x}^{2}}+lx+m\] Then, \[f(-k)=0\]and\[g(-k)=0\] \[\Rightarrow \]\[{{k}^{2}}-kp+q=0\]and \[{{k}^{2}}-kl+m=0\] \[\Rightarrow \]\[{{k}^{2}}=kp-q\] ?(i) and \[{{k}^{2}}=kl-m\] From (i) and (ii), we have \[kp-q=kl-m\] \[\Rightarrow \]\[k=\frac{q-m}{p-l}\Rightarrow k=\frac{m-q}{l-p}\]
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