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Solving Quadratic Equations by Factorization (II)

Solving Quadratic Equations by Factorization (II)
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2017-12-27 16:01
Coordinate Geometry
This example demonstrates how to solve quadratic equations not in standard form using factorization. Key math concepts include quadratic equations, factoring, and root finding. It is constructed using GeoGebra commands like RandomElement, Random, Simplify, Coefficients, RandomPolynomial, Factor, GCD, If, and involves objects such as sliders and text elements. Suitable for high school mathematics education to help students practice and master solving quadratic equations.

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. If(c / a < 0, "-" + (FractionText[abs(c / a)]), "" + (FractionText[abs(c / a)])) → text5
  15. If(d / b < 0, "-" + (FractionText[abs(d / b)]), "" + (FractionText[abs(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