solve` x^2 -3x +2=0`

Options

A. `-1`
B. 1
C. 2
D. 3

Answer

To solve the quadratic equation \( x^2 - 3x + 2 = 0 \), we can follow these steps:

### Step 1: Write the equation
We start with the given equation:
\[ x^2 - 3x + 2 = 0 \]

### Step 2: Factor the quadratic expression
We need to factor the quadratic expression. We look for two numbers that multiply to \( +2 \) (the constant term) and add up to \( -3 \) (the coefficient of \( x \)). The numbers that satisfy these conditions are \( -1 \) and \( -2 \).

Thus, we can rewrite the equation as:
\[ x^2 - 2x - x + 2 = 0 \]

### Step 3: Group the terms
Next, we group the terms:
\[ (x^2 - 2x) + (-x + 2) = 0 \]

### Step 4: Factor by grouping
Now we factor out the common terms from each group:
\[ x(x - 2) - 1(x - 2) = 0 \]

### Step 5: Factor out the common binomial
We can factor out the common binomial \( (x - 2) \):
\[ (x - 2)(x - 1) = 0 \]

### Step 6: Set each factor to zero
Now, we set each factor equal to zero:
1. \( x - 2 = 0 \) → \( x = 2 \)
2. \( x - 1 = 0 \) → \( x = 1 \)

### Step 7: Write the final solutions
The solutions to the equation \( x^2 - 3x + 2 = 0 \) are:
\[ x = 2 \quad \text{and} \quad x = 1 \]