Originally Posted by

**Dinkydoe** Then I wonder how you came to these relations

The only way you could have found these relations is by considering $\displaystyle (x-\alpha)(x-\beta)(x-\gamma) = x^3-(\alpha+\beta+\gamma)x^2+(\alpha\beta+\alpha\gamma +\beta\gamma)x - \alpha\beta\gamma = x^3 + 4x^2 + 3x + 2$

Then the relations you start out with follow.

After that you want an equation with roots $\displaystyle \alpha\gamma,\beta\gamma,\alpha\beta $

An equation that satisfies this property is: $\displaystyle (x-\alpha\gamma)(x-\beta\gamma)(x-\alpha\beta) = 0 $

But we like to know explicitly how this polynomial looks like from the relations we derived.

Thus we write out this factored form: This can be tenacious work but it's not that hard actually. Mathematics is 10 % inspiration, 90% perspiration.