If two equations ` x^(2) + ax + bc = 0 and x^(2) + bx + ca =0` have a common root, the find the condition and the quadratic with other roots of the equations.

Explanation

To solve the problem, we need to find the condition under which the two quadratic equations \( x^2 + ax + bc = 0 \) and \( x^2 + bx + ca = 0 \) have a common root. We will denote the common root as \( \alpha \).

### Step-by-Step Solution:

1. **Identify the Common Root**:
Let \( \alpha \) be the common root of both equations. Then, we can substitute \( \alpha \) into both equations:
\[
\alpha^2 + a\alpha + bc = 0 \quad \text{(1)}
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