Question
Let $$\alpha ,\beta $$ be the roots of the equation $$\left( {x - a} \right)\left( {x - b} \right) = c,c \ne 0.$$ Then the roots of the equation $$\left( {x - \alpha } \right)\left( {x - \beta } \right) + c = 0\,\,{\text{are}}$$
A.
$$a, c$$
B.
$$b, c$$
C.
$$a, b$$
D.
$$a + c, b + c$$
Answer :
$$a, b$$
Solution :
$$\eqalign{
& \alpha ,\beta \,\,{\text{are roots of the equation }}\left( {x - a} \right)\left( {x - b} \right) = c,c \ne 0 \cr
& \therefore \,\,\left( {x - a} \right)\left( {x - b} \right) - c = \left( {x - \alpha } \right)\left( {x - \beta } \right) \cr
& \Rightarrow \,\,\left( {x - \alpha } \right)\left( {x - \beta } \right) + c = \left( {x - a} \right)\left( {x - b} \right) \cr
& \Rightarrow \,\,{\text{roots of }}\left( {x - \alpha } \right)\left( {x - \beta } \right) + c = 0\,\,{\text{are }}\,a\,{\text{and }}b. \cr
& \therefore \,\,\left( {\text{C}} \right){\text{is the correct option}}{\text{.}} \cr} $$