Question

If $(x+k)$ is a common factor of $(x^2+px+q)$ and $(x^2+lx+m)$, then the value of $k$ is ____.

• A. $l+p$
• B. $m-q$
• C. $\frac{l-p}{m-q}$
• D. $\frac{m-q}{l-p}$

Answer 1

The correct option is D $\frac{m-q}{l-p}$

Let $x^2+px+q=0$ ....(1)

and $x^2+lx+m=0$ ....(2)

If both equations have the same factor $(x+k)$, then substracting equation (1) from (2), we get

$(p-l)x+(q-m)=0$

Common factor is $(x+k)$

Therefore putting $x=-k$ in above equation, we get,

$(p-l)(-k)+(q-m)=0\Rightarrow k=\frac{m-q}{l-p}$