Find the roots of quadrratic equation` x^2 - 3x +2`.

Answer

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

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

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

Thus, we can rewrite the quadratic 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 can factor each group:
\[ x(x - 2) - 1(x - 2) = 0 \]

### Step 5: Factor out the common term
Now, we can factor out the common term \((x - 2)\):
\[ (x - 1)(x - 2) = 0 \]

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

### Conclusion
The roots of the quadratic equation \(x^2 - 3x + 2 = 0\) are:
\[ x = 1 \quad \text{and} \quad x = 2 \]

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