Question

if α andβ are the roots of the equation (x-a)(x-b)+c=0,find the roots of the equation (x-α)(x-β)=c.

Answer 1

as we know:
α + ß = a + b (1)
αß = ab + c (2) 

Now, let A, B be the roots of 

(x-α)(x-ß) - c = 0 ... 1x² - (α+ß)x + (αß-c) = 0 

so, A + B = α + ß = a + b ... from (1) 

A·B = αß - c = (ab+c) - c = ab from (2) 

thus, A + B = a + b
A·B = ab 

The required roots are : a and b.