if roots of (x-p)(x-q) = c are a and b

what will be the roots of (x-a)(x-b) = -c

please explain

Ans:p,q

Solution: (x-p)(x-q)-c=0 has roots a and b=> ab=pq-c & a+b=p+q; 

similarly if s and t be the roots of (x-a)(x-b)=-c=>st=ab+c & s+t=a+b;(now wkt ab=pq-c=>st=pq)

therfore, s and t are p and q.

the answer is p and -q since in the first equation on equating we get a=c+b and b=c+q when we equate we get a-b=p-q which imples root of equaton 2 is p and -q

(x-p)(x-q)=c

x²-(p+q)x-c=0

hence,           a+b=p+q

 and               a.b=pq-c

                    a.b+c=p.q

by solving other eq we get

x²-(a+b)x+ab+c=0

thus        sum of roots=a+b=p+q

       product of roots=a.b+c=p.q

hence its roots are pand q