If ` alpha ` is one of the non real imaginary seventh roots of unity, then form the quadratic equation whose roots are given by ` alpha + alpha^(2) + alpha^(4) and alpha^(3) + alpha^(5) + alpha^(6)`

Explanation

To solve the problem, we need to find the quadratic equation whose roots are given by \( \alpha + \alpha^2 + \alpha^4 \) and \( \alpha^3 + \alpha^5 + \alpha^6 \), where \( \alpha \) is one of the non-real imaginary seventh roots of unity.

### Step-by-step Solution:

1. **Identify the seventh roots of unity**:
The seventh roots of unity are given by:
\[
\alpha_k = e^{i \frac{2\pi k}{7}} \quad \text{for } k = 0, 1, 2, \ldots, 6
...