Find the quadratic polynomial whose zeros are 3 and 4.

Answer

To find the quadratic polynomial whose zeros are 3 and 4, we can follow these steps:

### Step 1: Identify the zeros
The given zeros of the polynomial are \( \alpha = 3 \) and \( \beta = 4 \).

### Step 2: Calculate the sum and product of the zeros
- The sum of the zeros \( \alpha + \beta \) is:
\[ \alpha + \beta = 3 + 4 = 7 \]
- The product of the zeros \( \alpha \beta \) is:
\[ \alpha \beta = 3 \times 4 = 12 \]

### Step 3: Use the standard form of a quadratic polynomial
The standard form of a quadratic polynomial with zeros \( \alpha \) and \( \beta \) is given by:
\[ P(x) = x^2 - (\text{sum of zeros}) \cdot x + (\text{product of zeros}) \]
Substituting the values we found:
\[ P(x) = x^2 - (7)x + 12 \]

### Step 4: Write the polynomial
Thus, the quadratic polynomial is:
\[ P(x) = x^2 - 7x + 12 \]

### Final Answer
The quadratic polynomial whose zeros are 3 and 4 is:
\[ \boxed{x^2 - 7x + 12} \]

---