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 the common root.

### Step 1: Factor the first equation
The first equation is:
\[ x^2 - x - 12 = 0 \]
We can factor this equation. We look for two numbers that multiply to \(-12\) and add to \(-1\). These numbers are \(3\) and \(-4\).
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