The roots of the quadratic polynomial `x^2-5x+6=0` is:

Options

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

Answer

To find the roots of the quadratic polynomial \(x^2 - 5x + 6 = 0\), we can use the factorization method. Here are the steps to solve the equation:

### Step 1: Write the quadratic equation
The given quadratic polynomial is:
\[ x^2 - 5x + 6 = 0 \]

### Step 2: Factor the quadratic expression
We need to factor the expression \(x^2 - 5x + 6\). We look for two numbers that multiply to \(6\) (the constant term) and add up to \(-5\) (the coefficient of \(x\)). The numbers that satisfy this condition are \(-2\) and \(-3\).

Thus, we can write:
\[ x^2 - 5x + 6 = (x - 2)(x - 3) \]

### Step 3: Set each factor to zero
Now, we set each factor equal to zero to find the roots:
\[ x - 2 = 0 \quad \text{or} \quad x - 3 = 0 \]

### Step 4: Solve for \(x\)
Solving these equations gives us:
1. \(x - 2 = 0 \Rightarrow x = 2\)
2. \(x - 3 = 0 \Rightarrow x = 3\)

### Conclusion
The roots of the quadratic polynomial \(x^2 - 5x + 6 = 0\) are:
\[ x = 2 \quad \text{and} \quad x = 3 \]