Find the value of `alpha + beta` for the equation `x^2 + 8x+12 =0`

Answer

To find the value of \( \alpha + \beta \) for the quadratic equation \( x^2 + 8x + 12 = 0 \), we can follow these steps:

### Step 1: Identify the coefficients
The given quadratic equation is in the standard form \( ax^2 + bx + c = 0 \). Here, we can identify:
- \( a = 1 \)
- \( b = 8 \)
- \( c = 12 \)

### Step 2: Use the formula for the sum of the roots
The sum of the roots (or zeros) of a quadratic equation is given by the formula:
\[ \alpha + \beta = -\frac{b}{a} \]

### Step 3: Substitute the values into the formula
Now, we can substitute the values of \( b \) and \( a \) into the formula:
\[ \alpha + \beta = -\frac{8}{1} \]

### Step 4: Calculate the sum
Calculating the above expression gives:
\[ \alpha + \beta = -8 \]

### Final Answer
Thus, the value of \( \alpha + \beta \) is \( -8 \).

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