[从头学数学] 第149节 一元二次方程 小结与复习题

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入了筑基后期的修炼，
这次要修炼的目标是[一元二次方程 小结与复习题]。

正剧开始：

星历2016年03月23日 13:47:16, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起研究[一元二次方程 小结与复习题]。

<span style="font-size:18px;">		var equation = new Equation();
		
		var a = [196,0,-1];
		equation.quadratic(a);
		
		a = [4,12,9-81];
		equation.quadratic(a);
		
		a = [1,-7,-1];
		equation.quadratic(a);
		
		a = [2,3,-3];
		equation.quadratic(a);
		
		a = [1,-2,1-25];
		equation.quadratic(a);
		
		a = [2,-9,10];
		equation.quadratic(a);
		
		a = [1,2,-4];
		equation.quadratic(a);
		
		a = [16,0,-1];
		equation.quadratic(a);</span>

方程 196x^[2] + 0x + -1 = 0 =>
Δ = b^[2] - 4ac = 784 ;
方程的解为：x1 = -0.07142857142857142, x2 = 0.07142857142857142 ;
方程根与系数的关系：x1 + x2 = 0, x1 * x2 = -0.00510204081632653 ;

方程 4x^[2] + 12x + -72 = 0 =>
Δ = b^[2] - 4ac = 1296 ;
方程的解为：x1 = -6, x2 = 3 ;
方程根与系数的关系：x1 + x2 = -3, x1 * x2 = -18 ;

方程 1x^[2] + -7x + -1 = 0 =>
Δ = b^[2] - 4ac = 53 ;
方程的解为：x1 = -0.14005494464025903, x2 = 7.140054944640259 ;
方程根与系数的关系：x1 + x2 = 7, x1 * x2 = -0.9999999999999991 ;

方程 2x^[2] + 3x + -3 = 0 =>
Δ = b^[2] - 4ac = 33 ;
方程的解为：x1 = -2.186140661634507, x2 = 0.6861406616345072 ;
方程根与系数的关系：x1 + x2 = -1.5, x1 * x2 = -1.5 ;

方程 1x^[2] + -2x + -24 = 0 =>
Δ = b^[2] - 4ac = 100 ;
方程的解为：x1 = -4, x2 = 6 ;
方程根与系数的关系：x1 + x2 = 2, x1 * x2 = -24 ;

方程 2x^[2] + -9x + 10 = 0 =>
Δ = b^[2] - 4ac = 1 ;
方程的解为：x1 = 2, x2 = 2.5 ;
方程根与系数的关系：x1 + x2 = 4.5, x1 * x2 = 5 ;

方程 1x^[2] + 2x + -4 = 0 =>
Δ = b^[2] - 4ac = 20 ;
方程的解为：x1 = -3.23606797749979, x2 = 1.2360679774997898 ;
方程根与系数的关系：x1 + x2 = -2, x1 * x2 = -4.000000000000001 ;

方程 16x^[2] + 0x + -1 = 0 =>
Δ = b^[2] - 4ac = 64 ;
方程的解为：x1 = -0.25, x2 = 0.25 ;
方程根与系数的关系：x1 + x2 = 0, x1 * x2 = -0.0625 ;

<span style="font-size:18px;">		var equation = new Equation();
		
		var a = [1,-8,9.75];
		equation.quadratic(a);

		//(x-3)x=4
		a = [1,-3,-4];
		equation.quadratic(a);</span>

方程 1x^[2] + -8x + 9.75 = 0 =>
Δ = b^[2] - 4ac = 25 ;
方程的解为：x1 = 1.5, x2 = 6.5 ;
方程根与系数的关系：x1 + x2 = 8, x1 * x2 = 9.75 ;

方程 1x^[2] + -3x + -4 = 0 =>
Δ = b^[2] - 4ac = 25 ;
方程的解为：x1 = -1, x2 = 4 ;
方程根与系数的关系：x1 + x2 = 3, x1 * x2 = -4 ;

<span style="font-size:18px;">		var equation = new Equation();
		
		var a = [1,-5,-10];
		equation.quadratic(a);

		a = [2,7,1];
		equation.quadratic(a);
		
		a = [3,-2,-6];
		equation.quadratic(a);
		
		a = [1,-4,-7];
		equation.quadratic(a);</span>

方程 1x^[2] + -5x + -10 = 0 =>
Δ = b^[2] - 4ac = 65 ;
方程的解为：x1 = -1.5311288741492746, x2 = 6.531128874149275 ;
方程根与系数的关系：x1 + x2 = 5, x1 * x2 = -9.999999999999998 ;

方程 2x^[2] + 7x + 1 = 0 =>
Δ = b^[2] - 4ac = 41 ;
方程的解为：x1 = -3.350781059358212, x2 = -0.14921894064178787 ;
方程根与系数的关系：x1 + x2 = -3.5, x1 * x2 = 0.5000000000000001 ;

方程 3x^[2] + -2x + -6 = 0 =>
Δ = b^[2] - 4ac = 76 ;
方程的解为：x1 = -1.1196329811802246, x2 = 1.7862996478468913 ;
方程根与系数的关系：x1 + x2 = 0.6666666666666667, x1 * x2 = -2.0000000000000004 ;

方程 1x^[2] + -4x + -7 = 0 =>
Δ = b^[2] - 4ac = 44 ;
方程的解为：x1 = -1.3166247903553998, x2 = 5.3166247903554 ;
方程根与系数的关系：x1 + x2 = 4, x1 * x2 = -7 ;

<span style="font-size:18px;">		var equation = new Equation();
		
		//(x+x+2)*(x-1)/2 = 8
		var a = [1, 0, -9];
		equation.quadratic(a);</span>

方程 1x^[2] + 0x + -9 = 0 =>
Δ = b^[2] - 4ac = 36 ;
方程的解为：x1 = -3, x2 = 3 ;
方程根与系数的关系：x1 + x2 = 0, x1 * x2 = -9 ;

这是一个上底长3的梯形

		var r = 40;
		config.setSector(1,1,1,1);  
		config.graphPaper2D(0, 0, r);		
		config.axis2D(0, 0,180, 1);  
		
		var a = [[0, 0], [5,0],[0,2],[3,2]];
		shape.angleDraw([].concat(a), 'red', r);

		var equation = new Equation();
		
		//(5*5x+5*2x+10x2)*2 = 40
		var a = [20, 70,-40];
		equation.quadratic(a);

方程 20x^[2] + 70x + -40 = 0 =>
Δ = b^[2] - 4ac = 8100 ;
方程的解为：x1 = -4, x2 = 0.5 ;
方程根与系数的关系：x1 + x2 = -3.5, x1 * x2 = -2 ;

这个长方体长2.5，宽1, 高5

		var r = 20;
		config.setSector(1,1,1,1);  
		config.graphPaper2D(0, 0, r);		
		config.axis2D(0, 0,180, 1);  
		
		var x = 0, y = 0;
		var a = 2.5, b = 1, h = 5;
		var Sa = [[a, 0], [a, b], [0, 0], [0, b]];
		var Sb = [[0, 0], [a, 0], [0, h], [a, h]];
		var Sc = [[0, 0], [b, 0], [0, h], [b, h]];
		Sa = shape.angularSort(Sa);
		Sb = shape.angularSort(Sb);
		Sc = shape.angularSort(Sc);
		
		var transform = new Transform();
		
		shape.fillDraw([].concat(Sa), 'red', r);
		shape.fillDraw([].concat(transform.translate(Sb, 0, -h)), 'blue', r);
		shape.fillDraw([].concat(transform.translate(Sc, -b, -h)), 'green', r);
		shape.fillDraw([].concat(transform.translate(Sb, -a-b, -h)), 'blue', r);
		shape.fillDraw([].concat(transform.translate(Sc, -a-b-b, -h)), 'green', r);
		shape.fillDraw([].concat(transform.translate(Sa, 0, -h-b)), 'red', r);

		var equation = new Equation();
		
		//x(x-1)/2 = 15
		var a = [1, -1, -30];
		equation.quadratic(a);

方程 1x^[2] + -1x + -30 = 0 =>
Δ = b^[2] - 4ac = 121 ;
方程的解为：x1 = -5, x2 = 6 ;
方程根与系数的关系：x1 + x2 = 1, x1 * x2 = -30 ;

		var equation = new Equation();
		
		//x(20-2x) = 50
		var a = [-2,20,-50];
		equation.quadratic(a);

方程 -2x^[2] + 20x + -50 = 0 =>
Δ = b^[2] - 4ac = 0 ;
方程的解为：x1 = x2 = 5 ;
方程根与系数的关系：x1 + x2 = 10, x1 * x2 = 25 ;

				
		var equation = new Equation();
		
		//x(40-2x) = 75*2
		var a = [-2,40,-150];
		equation.quadratic(a);
		
		a = [-2,40,-220];
		equation.quadratic(a);

方程 -2x^[2] + 40x + -150 = 0 =>
Δ = b^[2] - 4ac = 400 ;
方程的解为：x1 = 15, x2 = 5 ;
方程根与系数的关系：x1 + x2 = 20, x1 * x2 = 75 ;

方程 -2x^[2] + 40x + -220 = 0 =>
Δ = b^[2] - 4ac = -160 ;
没有实数解。

		var equation = new Equation();
		
		//80*2*x+140x-2x2 = 140*80/6
		var a = [2, -300,140*80/6];
		equation.quadratic(a);

方程 2x^[2] + -300x + 1866.6666666666667 = 0 =>
Δ = b^[2] - 4ac = 75066.66666666667 ;
方程的解为：x1 = 6.504258039884945, x2 = 143.49574196011505 ;
方程根与系数的关系：x1 + x2 = 150, x1 * x2 = 933.3333333333338 ;

		var equation = new Equation();
		
		//(5+5-1.25x)/2*x=5
		var a = [-1.25, 10, -10];
		equation.quadratic(a);

方程 -1.25x^[2] + 10x + -10 = 0 =>
Δ = b^[2] - 4ac = 50 ;
方程的解为：x1 = 6.82842712474619, x2 = 1.1715728752538097 ;
方程根与系数的关系：x1 + x2 = 8, x1 * x2 = 7.999999999999998 ;

本节到此结束，欲知后事如何，请看下回分解。