Find the discriminant of the equation `x^(2) +3x+2= 0`.

Answer

To find the discriminant of the quadratic equation \(x^2 + 3x + 2 = 0\), we will follow these steps:

### Step 1: Identify the coefficients
The standard form of a quadratic equation is \(ax^2 + bx + c = 0\). In our equation:
- \(a = 1\) (coefficient of \(x^2\))
- \(b = 3\) (coefficient of \(x\))
- \(c = 2\) (constant term)

### Step 2: Write the formula for the discriminant
The discriminant \(D\) of a quadratic equation is given by the formula:
\[ D = b^2 - 4ac \]

### Step 3: Substitute the values of \(a\), \(b\), and \(c\) into the formula
Now we will substitute \(a\), \(b\), and \(c\) into the discriminant formula:
\[ D = (3)^2 - 4 \cdot (1) \cdot (2) \]

### Step 4: Calculate \(b^2\)
Calculating \(b^2\):
\[ D = 9 - 4 \cdot (1) \cdot (2) \]

### Step 5: Calculate \(4ac\)
Calculating \(4ac\):
\[ D = 9 - 8 \]

### Step 6: Final calculation
Now, we perform the final calculation:
\[ D = 1 \]

### Conclusion
The discriminant of the equation \(x^2 + 3x + 2 = 0\) is \(1\).

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