Find a quadratic polynomial with the given number as the sum and product of its zeroes respectively are 3 and 2.

Explanation

To find a quadratic polynomial given that the sum of its zeroes is 3 and the product of its zeroes is 2, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the sum and product of the zeroes**:
Let the zeroes of the polynomial be denoted as α (alpha) and β (beta).
- Given:
- Sum of the zeroes (α + β) = 3
- Product of the zeroes (α * β) = 2

2. **Use the standard form of a quadratic polynomial**:
The standard form of a quadratic polynomial with zeroes α and β is given by:
\[ P(x) = x^2 - (α + β)x + (α * β) \]

3. **Substitute the values of the sum and product**:
Substitute the known values into the polynomial:
- Sum of zeroes: α + β = 3
- Product of zeroes: α * β = 2

Therefore, we can write:
\[ P(x) = x^2 - (3)x + (2) \]

4. **Simplify the polynomial**:
Simplifying the expression gives:
\[ P(x) = x^2 - 3x + 2 \]

5. **Final Result**:
The required quadratic polynomial is:
\[ P(x) = x^2 - 3x + 2 \]