if roots of equation (n-p)(n-q)=r, in n are l and m, then the roots of equation (n-l)(n-m)+r=0 is p and q..prove it plz

(l-p)(m-q)=r, this implies that (p-l)(q-m)=-(-r)=r

(n-m)(n-q)=r            l & m are roots

n²-n(p+q) + pq - r =0

p+q= l+m                      (sum of roots)

pq=lm + r                   (product of roots) 

now eqn whose roots are p & q are given by

 n²-(p+q)n + pq

=n²-(l+m) + lm +r

=(n-l)(n-m) +r

Approved