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

Step-by-step solution

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