Write the solution set of the equation `x^2+ x -2 = 0` in roster form.

Options

A. `{-1,-2}`
B. `{1,2}`
C. `{1,-2}`
D. `{-1,2}`

Explanation

To solve the equation \(x^2 + x - 2 = 0\) and express the solution set in roster form, we will follow these steps:

### Step 1: Write the equation
We start with the quadratic equation:
\[ x^2 + x - 2 = 0 \]

### Step 2: Factor the quadratic equation
To solve the equation, we will factor it. We need two numbers that multiply to \(-2\) (the constant term) and add to \(1\) (the coefficient of \(x\)). The numbers that satisfy these conditions are \(2\) and \(-1\).

Thus, we can factor the equation as:
\[ (x + 2)(x - 1) = 0 \]

### Step 3: Set each factor to zero
Now, we set each factor equal to zero:
1. \(x + 2 = 0\)
2. \(x - 1 = 0\)

### Step 4: Solve for \(x\)
Solving these equations gives us:
1. From \(x + 2 = 0\), we find \(x = -2\).
2. From \(x - 1 = 0\), we find \(x = 1\).

### Step 5: Write the solution set in roster form
The solutions we found are \(x = -2\) and \(x = 1\). Therefore, the solution set in roster form is:
\[ A = \{-2, 1\} \]

### Final Answer
The solution set of the equation \(x^2 + x - 2 = 0\) in roster form is:
\[ A = \{-2, 1\} \]

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