If the sum of the roots of the equation $\displaystyle cx^2 - (1 + c)x + 3c + 2 = 0 $ is equal to twice the product of the roots, find the value of c and the two roots.

$\displaystyle \alpha + \beta = \frac{1+c}{c}$

$\displaystyle \alpha\beta = \frac{3c + 2}{c}$

Then, I solved the rest and finally I got,

c(5c + 3) = 0

So, $\displaystyle c = 0 $ or $\displaystyle c = \frac{-3}{5} $

But in my answer book, the answer for c is $\displaystyle \frac{-3}{5}$ only. Why is it so?