If `A = {x:f(x) =0} and B = {x:g(x) = 0}`, then `A uu B` will be the set of roots of the equation

Options

A. `{f(x)}^(2)+{g(x)}^(2) = 0`
B. `(f(x))/(g(x))`
C. `(g(x))/(f(x))`
D. none of these

Answer

To solve the problem, we need to understand the implications of the sets \( A \) and \( B \) defined by the equations \( f(x) = 0 \) and \( g(x) = 0 \).

### Step-by-Step Solution:

1. **Define the Sets**:
- Let \( A = \{ x : f(x) = 0 \} \) be the set of roots of the function \( f(x) \).
- Let \( B = \{ x : g(x) = 0 \} \) be the set of roots of the function \( g(x) \).

2. **Union of the Sets**:
- The union of sets \( A \) and \( B \), denoted \( A \cup B \), will include all elements that are in either set \( A \) or set \( B \). Therefore, \( A \cup B = \{ x : f(x) = 0 \text{ or } g(x) = 0 \} \).

3. **Roots of the Combined Equation**:
- The combined equation that has roots in both sets can be represented as \( f(x) = 0 \) or \( g(x) = 0 \). This means that the roots of the equation formed by taking the union of the roots from both functions will be the values of \( x \) that satisfy either \( f(x) = 0 \) or \( g(x) = 0 \).

4. **Conclusion**:
- Thus, \( A \cup B \) will be the set of all roots of the equation formed by the union of the roots of \( f(x) \) and \( g(x) \).

### Final Answer:
The set \( A \cup B \) will be the set of roots of the equation \( f(x) = 0 \) or \( g(x) = 0 \).

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