If the sum of the roots of a quadratic equation is 3 and the product is 2. then the equation is :

Options

A. `2x^(2) - x + 3 = 0`
B. `x^(2) - 3x + 2 =0`
C. `x^(2) + 3x + 2 = 0`
D. `x^(2) + 3x - 2 = 0`

Answer

To find the quadratic equation based on the given sum and product of its roots, we can use the standard form of a quadratic equation derived from its roots.

### Step-by-step Solution:

1. **Understanding the relationship**:
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), if the roots are \( r_1 \) and \( r_2 \), then:
- The sum of the roots \( r_1 + r_2 = -\frac{b}{a} \)
- The product of the roots \( r_1 \cdot r_2 = \frac{c}{a} \)

2. **Given values**:
- Sum of the roots \( r_1 + r_2 = 3 \)
- Product of the roots \( r_1 \cdot r_2 = 2 \)

3. **Setting up the equation**:
We can express the quadratic equation using the sum and product of the roots:
\[ x^2 - (r_1 + r_2)x + (r_1 \cdot r_2) = 0 \]

4. **Substituting the values**:
Substituting the given sum and product into the equation:
\[ x^2 - (3)x + (2) = 0 \]

5. **Final form of the equation**:
This simplifies to:
\[ x^2 - 3x + 2 = 0 \]

### Final Answer:
The quadratic equation is:
\[ x^2 - 3x + 2 = 0 \]

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