Find the quadratic polynomial whose zeros are - 3 and -5.

Answer

To find the quadratic polynomial whose zeros are -3 and -5, we can follow these steps:

### Step 1: Identify the zeros
Let the zeros be:
- α = -3
- β = -5

### Step 2: Calculate the sum of the zeros
The sum of the zeros (α + β) is calculated as follows:
\[ \text{Sum of zeros} = α + β = -3 + (-5) = -3 - 5 = -8 \]

### Step 3: Calculate the product of the zeros
The product of the zeros (α × β) is calculated as follows:
\[ \text{Product of zeros} = α × β = -3 × -5 = 15 \]

### Step 4: Write the quadratic polynomial
The standard form of a quadratic polynomial with zeros α and β is given by:
\[ P(x) = x^2 - (\text{sum of zeros}) \cdot x + (\text{product of zeros}) \]
Substituting the values we found:
\[ P(x) = x^2 - (-8)x + 15 \]
This simplifies to:
\[ P(x) = x^2 + 8x + 15 \]

### Final Answer
The required quadratic polynomial is:
\[ \boxed{x^2 + 8x + 15} \]

---