Question

If HCF of algebraic expressions $(x^2+px+q)$ and $(x^2+lx+m)$ is $(x+k)$, then find the value of k.

Answer 1

$\begin{array}{c}x=-k\\ x^2+px+q=0\\ putthevaluofx\\ \Rightarrow k^2-kp+q=\mathrm{0...}\left(1\right)\\ x^2+lx+m=0\\ \Rightarrow k^2-lk+m=\mathrm{0....}\left(2\right)\\ fromeq\left(1\right)and\left(2\right)\\ k^2-kp+q=\mathrm{0.....}\left(1\right)\\ k^2-lk+m=\mathrm{0......}\left(2\right)\\ k\left(l-p\right)=m-q\\ k=\left(\frac{m-q}{l-p}\right)\\ Ans.k=\frac{m-q}{l-p}\end{array}$