解线性因子的乘积为零的方程

几何画板及绘图内容加载中，请稍等……

2016-11-03 14:31

几何作图

①本范例演示解线性因子乘积为零的方程，通过可视化展示零因子定理；②涉及核心数学概念包括零因子定理、线性方程、因式分解；③构造要点：使用 GeoGebra 命令 If, RandomElement, Simplify, Coefficients, Factor, GCD, FractionText 等，对象包括 level, a, c, b, d, final, right, list1, left, f, gcdac, gcdbd, factor1, factor2, text5, text6, e, divideoutgcd, g, button1, button2, step1, button3, button4, button5, step2, step3, step4, text8, text1, text2, button6, step5, text9, text10, text11, button7, numeqns, text4, text3；④适合高中数学教学或学生自学，帮助理解方程解的几何意义。

GeoGebra 命令及参数

If(level ≟ 1, RandomElement[{1, 1, -3, -1, -2, 1, -1, 1, 1, 2, 3, 1, 1}], RandomElement[{-3, 1, -2, 1, -1, 1, 1, 2, 3, 1}]) → a
If(level ≟ 1, 0, If[level ≟ 2, RandomElement[{-4, -3, -2, -1, 1, 2, 3, 4}], RandomElement[{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]]) → c
RandomElement({-3, 1, -2, 1, -1, 1, 1, 2, 3, 1}) → b
If(level < 2, RandomElement[{-4, -3, -2, -1, 1, 2, 3, 4}], RandomElement[{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]) → d
Simplify((((a * x) - c) * ((b * x) - d))) → final
RandomElement({0, 0, 1, 0, 0, 3, 0, 0, 4, 0, 0, 2}) → right
Coefficients(final) → list1
Simplify(final(x) + (right * x)) → left
Factor(final) → f
GCD(a, c) → gcdac
GCD(b, d) → gcdbd
Simplify(If[a < 0, ((a * x) - c) / ((-gcdac)), ((a * x) - c) / gcdac]) → factor1
Simplify(If[b < 0, ((b * x) - d) / ((-gcdbd)), ((b * x) - d) / gcdbd]) → factor2
FractionText(c / a) → text5
FractionText(d / b) → text6
If(Element[list1, 1] < 0, (-GCD[Coefficients[final]]), GCD[Coefficients[final]]) → e
Simplify(final(x) / e) → divideoutgcd
Factor(divideoutgcd) → g