Question

let alpha beta be the root of the equation x minus A into x minus b is equal to C C is not equal to zero then the root of the equation x minus 1 into x minus beta + C is equal to zero

Answer 1

(x – \alpha)(x – \beta)=c

x2 – (\alpha + \beta)x +\alpha \beta = c (eqn 1 )

also

(x-a)(x-b) +c=0

x2 – (a+b)x +ab + c = 0

\alpha +\beta =a+b

\alpha\beta = ab + c

now eqn 1 becomes

x2 – (a+b)x + ab + c = c

x2 – (a+b)x + ab = 0

and roots of this equation are a and b