2011/017) if ( p and q) are roots of equation (x-a)(x-b) = c then

-->

Roots of equation (x-p)(x-q) + c are

a) a c

b) bc

c) a,b

d) (a+c), (b+c)

solution

-->

we have

(x-a)(x-b)) - c = x^2- (a+b) x+ (ab-c)

As p and q are roots so p+ q = a + b …1

and pq = ab – c or pq + c = ab …2

Now

(x-p)(x-q) + c = x^2 - (p+ q) x + (pq + c)

= x^2-(a+b)x + ab = (x-a)(x-b) ( from 1 and 2)

So roots are a and b

hence ans is c)