Solve x² − 5x + 6 = 0
This quadratic factors cleanly. Look for two numbers whose product is 6 and whose sum is −5.
Problemx² − 5x + 6 = 0
Show detailed solution
Answer: x = 2 or x = 3
Step 1: factor the quadratic
The numbers are −2 and −3, so x² − 5x + 6 = (x − 2)(x − 3).
Step 2: use the zero-product property
If (x − 2)(x − 3) = 0, then either x − 2 = 0 or x − 3 = 0.
Step 3: solve each equation
From x − 2 = 0, get x = 2. From x − 3 = 0, get x = 3.
Step 4: check both roots
For x = 2: 4 − 10 + 6 = 0. For x = 3: 9 − 15 + 6 = 0. Both satisfy the original equation.