Find the value of `lamda` so that the equations `x^(2)-x-12=0` and `lamdax^(2)+10x+3=0` may have one root in common. Also, find the common root.

Explanation

To solve the problem, we need to find the value of \( \lambda \) such that the equations \( x^2 - x - 12 = 0 \) and \( \lambda x^2 + 10x + 3 = 0 \) have one root in common. We will also find that common root.

### Step 1: Find the roots of the first equation
The first equation is:
\[ x^2 - x - 12 = 0 \]
We can factor this equation:
...