If m and n are the roots of the equation (x+p)(x+q)-k=0 , then the...

Here m and n are the roots of equation. $$\begin{aligned} & (x+p)(x+q)-k=0 \\ & x^2+x(p+q)+p q-k=0...(i) \end{aligned}$$ If m and n are the roots of equation, then $$\begin{array}{ll} & (x-m)(x-n)=0 \\ \therefore \quad & x^2-(m+n) x+m n=0...(ii) \end{array}$$Now equation (i) should be equal to equation (ii), Now, we have to find roots of (x-m)(x-n)+k=0$$\begin{aligned}& x²-(m+n) x+m n+k=0 \\ & x²+(p+q) x+(p q-k)+k=0 \\ & x²+(p+q) x+p q=0 \\ & x²+p x+q x+p q=0 \\ & x(x+p)+q(x+p)=0 \end{aligned}$$$$\begin{array}{ll}\therefore& x+q=0 \text{ or } x+p=0 \\ \therefore & x=-q\text{ and } x=-p \\ \therefore &\text{ Option (C) is correct. }\end{array}$$