Viète's Formulas/Examples/Sum 4, Product 8

Example of Use of Viète's Formulas
Let $z_1$ and $z_2$ be two numbers whose sum is $4$ and whose product is $8$.

Then:

Proof
Let $z_1$ and $z_2$ be the roots of the quadratic equation:
 * $z^2 + b z + c = 0$

From Viète's Formulas:

and so $z_1$ and $z_2$ are the roots of the quadratic equation: