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Factoring to Find Roots Practice

Factoring to Find Roots Practice
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2016-06-15 06:39
FunctionCalculus
This example demonstrates how to find the roots of a quadratic equation by factoring. Core math concepts include quadratic equations, factoring, and root properties. Construction highlights the use of GeoGebra commands like RandomElement, Random, Simplify, Coefficients, RandomPolynomial, Factor, GCD, FractionText, If, and objects such as a, d, c, b, final, list1. Suitable for high school mathematics teaching and practice.

GeoGebra Commands & Parameters

  1. RandomElement({-3, -2, -1, 1, 2, 3}) → a
  2. Random(-10, 10) → d
  3. Random(-10, 10) → c
  4. RandomElement({-3, -2, -1, 1, 2, 3}) → b
  5. Simplify((((a * x) - c) * ((b * x) - d))) → final
  6. Coefficients(final) → list1
  7. RandomPolynomial(2, -7, 7) → right
  8. Simplify(final(x) + right(x)) → left
  9. Factor(final) → f
  10. GCD(a, c) → gcdac
  11. GCD(b, d) → gcdbd
  12. Simplify(If[a < 0, ((a * x) - c) / ((-gcdac)), ((a * x) - c) / gcdac]) → factor1
  13. Simplify(If[b < 0, ((b * x) - d) / ((-gcdbd)), ((b * x) - d) / gcdbd]) → factor2
  14. FractionText(c / a) → text5
  15. FractionText(d / b) → text6
  16. If(Element[list1, 1] < 0, (-GCD[Coefficients[final]]), GCD[Coefficients[final]]) → e
  17. Simplify(final(x) / e) → divideoutgcd
  18. Factor(divideoutgcd) → g