Quadratic equations

Choose a suitable method, solve a quadratic, and check every solution and contextual condition.

Meaning

A quadratic equation simplifies to with Use factorization, square roots, completing the square, or the quadratic formula as appropriate.

Example

factors as so or A zero product must have at least one zero factor.Here factorization is convenient because −2 and −3 have sum −5 and product 6. Substituting 2 and 3 into the original expression checks that both give zero.You may set each factor to zero only when their product is zero. Giving just one of two solutions does not give all solutions.

Practice for this concept

Scope and references

Topics

Factorization, square-root methods, completing the square, the quadratic formula

Learning goal

Choose a suitable method, solve a quadratic, and check every solution and contextual condition.

Helpful background

Explore factorization or square roots as the form requires; learning every method first is unnecessary.

Simple quadratic-equation practice

Does not cover the quadratic formula, complex roots, or all quadratic equations.

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