Find a quadratic polynomial with the given number as the sum and product of its zeroes respectively are 5 and 3.

Explanation

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

### Step 1: Identify the sum and product of the zeroes
Let the zeroes of the polynomial be α (alpha) and β (beta). According to the problem:
- The sum of the zeroes (α + β) is given as 5.
- The product of the zeroes (α * β) is given as 3.

### Step 2: Use the standard form of a quadratic polynomial
The standard form of a quadratic polynomial can be expressed as:
\[ P(x) = x^2 - (α + β)x + (α * β) \]

### Step 3: Substitute the values of the sum and product into the polynomial
Now, substituting the values we have:
- α + β = 5
- α * β = 3

So, we can write:
\[ P(x) = x^2 - (5)x + (3) \]

### Step 4: Simplify the polynomial
Now, simplifying the expression:
\[ P(x) = x^2 - 5x + 3 \]

### Final Answer
Thus, the quadratic polynomial is:
\[ P(x) = x^2 - 5x + 3 \]

---