If the two factors of any quadratic equation are `(x+sqrt3)` and `(x-sqrt3)` , how many such equations are possible?

Options

A. A)0
B. B)1
C. C)2
D. D)infinite

Answer

To solve the problem, we need to find the quadratic equation formed by the given factors and determine how many such equations are possible.

### Step-by-step Solution:

1. **Identify the Factors**: The given factors of the quadratic equation are \( (x + \sqrt{3}) \) and \( (x - \sqrt{3}) \).

2. **Form the Quadratic Equation**: To form the quadratic equation from the factors, we multiply them:
\[ (x + \sqrt{3})(x - \sqrt{3}) \]

3. **Apply the Difference of Squares Formula**: The multiplication of these factors can be simplified using the difference of squares formula:
\[ (a + b)(a - b) = a^2 - b^2 \]
Here, \( a = x \) and \( b = \sqrt{3} \). Thus, we have:
\[ x^2 - (\sqrt{3})^2 = x^2 - 3 \]

4. **Write the Quadratic Equation**: The equation can now be written as:
\[ x^2 - 3 = 0 \]

5. **Determine the Number of Equations**: Since the factors \( (x + \sqrt{3}) \) and \( (x - \sqrt{3}) \) uniquely determine the quadratic equation \( x^2 - 3 = 0 \), there is only one such quadratic equation possible.

### Conclusion:
Thus, the number of such equations possible is **1**.