A quadratic can have more than one root
A quadratic equation in one variable simplifies to ax² + bx + c = 0, where a is not zero. Its highest power of the variable is 2. Its real solutions correspond to where the related graph meets the horizontal axis; there can be two, one, or no real roots.
Choose a method that fits the expression
Factoring is useful when the expression can be written as a product of simple factors. Completing the square and the quadratic formula handle other cases. The zero-product rule applies once the product equals zero.
A mistake to avoid
Do not assume every quadratic factors neatly over the integers, and do not discard one factor’s solution. An equation such as ab = 6 does not allow the same zero-product reasoning as ab = 0.
Worked example
Solve x² − 5x + 6 = 0
The expression factors as (x − 2)(x − 3). A product is zero when at least one factor is zero, so x = 2 or x = 3. Substituting either value into x² − 5x + 6 gives 0.