Find the sum and product of roots of `x^(2)+7x+12=0`

Answer

To find the sum and product of the roots of the quadratic equation \( x^2 + 7x + 12 = 0 \), we can follow these steps:

### Step 1: Identify the coefficients
The standard form of a quadratic equation is \( ax^2 + bx + c = 0 \). Here, we have:
- \( a = 1 \)
- \( b = 7 \)
- \( c = 12 \)

### Step 2: Use the formulas for sum and product of roots
For a quadratic equation \( ax^2 + bx + c = 0 \):
- The sum of the roots \( \alpha + \beta = -\frac{b}{a} \)
- The product of the roots \( \alpha \beta = \frac{c}{a} \)

### Step 3: Calculate the sum of the roots
Using the formula for the sum of the roots:
\[ \alpha + \beta = -\frac{b}{a} = -\frac{7}{1} = -7 \]

### Step 4: Calculate the product of the roots
Using the formula for the product of the roots:
\[ \alpha \beta = \frac{c}{a} = \frac{12}{1} = 12 \]

### Conclusion
Thus, the sum of the roots is \( -7 \) and the product of the roots is \( 12 \).

### Summary
- Sum of roots: \( -7 \)
- Product of roots: \( 12 \)

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