If `alpha & beta ` are the roots of the equation `a x^2 + b x + c = 0,` then `(1 + alpha + alpha^2) (1 + beta + beta^2) =`

Options

A. `1/a^2(a^2 -ab-b^2-ac-bc- c^2)`
B. `1/a^2(a^2 -ab+b^2-ac+bc+ c^2)`
C. `1/a^2(a^2 -ab+b^2-ac-bc+ c^2)`
D. `1/a^2(a^2 +ab+b^2-ac-bc+ c^2)`

Answer

C