# Thread: [SOLVED] Finding the unknown c?

1. ## [SOLVED] Finding the unknown c?

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

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

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

Then, I solved the rest and finally I got,

c(5c + 3) = 0

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

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

2. When c=0, the equation is no longer a quadratic. Hence that root is rejected.