Solution
= Solution
The sum of squared roots is $c_1^2-2c_2$. The sum of their pairwise products is
$$
(\alpha_1\alpha_2+\alpha_2\alpha_3+\alpha_3\alpha_1)^2
-2\alpha_1\alpha_2\alpha_3(\alpha_1+\alpha_2+\alpha_3)
=c_2^2-2c_1c_3.
$$
Their product is $c_3^2$. Thus the required <monic polynomial> is
$$
\boxed{X^3+(2c_2-c_1^2)X^2+(c_2^2-2c_1c_3)X-c_3^2.}
$$