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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
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
if answer is p and q then u can follow the following steps
first make the first equation a standard equation i.e. (x-p) (x-q) - c = 0
a and b are it''s root therefore (x-p) (x-q) - c = (x-a) (x-b)
now transfer c to RHS (x-p) (x-q) = (x-a) (x-b) + c ...........1
now observe your second equation it is simply (x-a) (x-b) + c = 0.........2
FROM 1 AND 2 u can clearly see that p and q are it''s root
HOPE U UNDERSTAND
The Answer is p,q. (Personal Note :Please vote this, if this helped. If not, Let me Know)
soln: (x-p)(x-q)=c has a,b as roots. This can be expanded as, : X2 -X(p+q)+pq-c=0
from the above eqn => (sum of roots)ie, a+b=p+q ---------(1)
&(product of roots)ie, ab=pq-c------(2)
Now, Expanding this equation (x-a)(x-b)=-c we get X2-X(a+b)+ab+c=0
therfore, (if s and t are the roots of the above eqn) => s+t=a+b;(sumof roots)--------(3)
also, st=ab+c;(prod of roots)-------(4)
comparing (1) and (3)=> a+b=p+q=s+t=>s+t=p+q-------(5)
substituting (2) in (4)=> st=(pq-c)+c=pq=>st=pq--------(6)
from (5) and(6) we can conclude that the roots reqd are s=p.t=q ie, p,q are the roots of the eqn .
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