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


2 Answers

Rohit Singh
15 Points
11 years ago

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


pvn kumar
32 Points
11 years ago

The Answer is p,q. (Personal Note :Please vote this, if this helped. If not, Let me KnowSmile)

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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