Algebra 1 · Unit 9 · Topic 9.5
Choosing Quadratic Methods and Interpreting Roots
Quadratic models can have mathematically valid roots that are excluded by a physical domain.
Definition and explanation
Quadratic models can have mathematically valid roots that are excluded by a physical domain. Choose factoring, square roots, completing the square, or the quadratic formula based on the equation's form, then interpret the roots in context.
Worked example
A rectangle has width w and length w + 3 meters, with area 40 m². Then w(w + 3) = 40, or (w + 8)(w − 5) = 0. Reject w = −8 because a length must be positive; w = 5 gives length 8 and area 40.
Common mistake
Do not report every algebraic root as a physical answer without checking units and domain.
Key takeaway
Quadratic models can have mathematically valid roots that are excluded by a physical domain.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.