Find the quadratic equation whose roots are, `-3, 5`

Answer

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

### Step 1: Identify the roots
The roots given are:
- \( \alpha = -3 \)
- \( \beta = 5 \)

### Step 2: Calculate the sum of the roots
The sum of the roots \( S \) is calculated as:
\[ S = \alpha + \beta = -3 + 5 = 2 \]

### Step 3: Calculate the product of the roots
The product of the roots \( P \) is calculated as:
\[ P = \alpha \cdot \beta = -3 \cdot 5 = -15 \]

### Step 4: Write the quadratic equation
The standard form of a quadratic equation with roots \( \alpha \) and \( \beta \) is:
\[ x^2 - Sx + P = 0 \]
Substituting the values of \( S \) and \( P \):
\[ x^2 - 2x - 15 = 0 \]

### Step 5: Finalize the quadratic equation
Thus, the quadratic equation whose roots are -3 and 5 is:
\[ \boxed{x^2 - 2x - 15 = 0} \]

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