UPSC NDA I 2015 Mathematics Solved Paper

Consider the equation
(x+p)(x+q)−k=0
x2+(p+q)x+pq−k=0
We get
p+q=−(m+n)
pq−k=mn...(i)
Now, consider the equations whose roots are required to be found out.
(x−m)(x−n)+k=0
x2−(m+n)x+mn+k=0
Substituting the value of ‘m’ and ‘n’ in the above equations, we get
x2−(−(p+q))x+pq−k+k=0
x2+(p+q)x+pq=0
(x+p)(x+q)=0
x=−p,x=−q