What are the roots of the polynomial x^2 - 5x + 6?

What are the roots of the polynomial x^2 - 5x + 6?

Step 1: Write down the polynomial you want to find the roots for: x^2 - 5x + 6.
Step 2: Look for two numbers that multiply to the constant term (6) and add up to the coefficient of the x term (-5).
Step 3: The two numbers that work are -2 and -3 because (-2) * (-3) = 6 and (-2) + (-3) = -5.
Step 4: Rewrite the polynomial using these two numbers: x^2 - 5x + 6 = (x - 2)(x - 3).
Step 5: Set each factor equal to zero: x - 2 = 0 and x - 3 = 0.
Step 6: Solve each equation: For x - 2 = 0, x = 2. For x - 3 = 0, x = 3.
Step 7: The roots of the polynomial are x = 2 and x = 3.

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