AlgebraMedium
Solve x² − 5x + 6 = 0
Factor a quadratic equation, apply the zero-product property, and verify both roots.
Method: Factoring and zero-product property
Step-by-step solution
- 1
Find a factor pair
The numbers −2 and −3 multiply to 6 and add to −5.
- 2
Factor
Rewrite the equation as a product equal to zero.
- 3
Solve each factor
A product is zero when at least one factor is zero.
- 4
Verify
Substituting 2 or 3 into the original quadratic gives zero.
Final answer
Both roots are valid and the discriminant is positive, consistent with two distinct real solutions.
Common mistake
Finding only one factor misses the second solution.
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Quadratic Solver
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