Not that complex

Let the polynomial $x^{2}+x+1$ have roots $\alpha$ and $\beta$ . Then there exists a polynomial with the roots $\alpha^{2}$ and $\beta^{2}$ in the form of $ax^2+bx+c$ , where $a$ , $b$ and $c$ are all integers, with $a$ begin positive and $\gcd(a,b,c) = 1$ .

Find $a+b+c$ .