[从头学数学] 第148节 一元二次方程

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]。

正剧开始：

星历2016年03月23日 11:12:44, 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]。

这是[机器小伟]刚从[人叫板老师]那里拿到的筑基后期的上半层功法。

为了能更好的修炼，这次阿伟又给小伟做了一个小工具：

<span style="font-size:18px;">function Equation() {
	this.quadratic = function(array) {
		//array = [a, b, c]
		//满足ax2 + bx + c = 0 (a!=0)
		var a = array[0], b = array[1], c = array[2];
		var p = 0, q = 0, delta = 0;
		var x1 = 0, x2 = 0;
		var s = '';
		
		if (a == 0) {
			s = '方程 '+b.toString()+'x + '+c.toString()+' = 0  =>';
			document.write(s+'<br/>');
			x1 = -c / b;
			s = '方程的解为：x =  '+x1.toString()+' ;';
		}
		else {
			s = '方程 '+a.toString()+'x^[2] + '+b.toString()+'x + '+c.toString()+' = 0  =>';
			document.write(s+'<br/>');
			delta = b*b-4*a*c;
			s = 'Δ = b^[2] - 4ac = ' + delta.toString()+' ;';
			document.write(s+'<br/>');
			
			if (delta < 0) {
				s = '没有实数解。';
				document.write(s+'<br/>');
			}
			else {
				if (Math.abs(delta) < 0.000001) {
					x1 = x2 = -b/(2*a);
					s = '方程的解为：x1 = x2 = '+x1.toString()+' ;';
				}
				else if (delta > 0) {
<span style="white-space:pre">					</span>x1 = (-b-Math.sqrt(delta))/(2*a);
<span style="white-space:pre">					</span>x2 = (-b+Math.sqrt(delta))/(2*a);
					s = '方程的解为：x1 = '+x1.toString()+'x2 = '+x2.toString()+' ;';
				}
				document.write(s+'<br/>');
				
				p = x1+x2;
				q = x1*x2;
				
				s = '方程根与系数的关系：x1 + x2 = ' + p.toString()+', x1 * x2 = '+q.toString()+' ;';
				document.write(s+'<br/>');
				document.write(''+'<br/>');
			}
		}
		
	}
}</span>

有了它，小伟应该可以省去不少麻烦的。

<span style="font-size:18px;">		var equation = new Equation();
		
		var a = [1, 2, -4];
		equation.quadratic(a);

</span>

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 ;

		var equation = new Equation();
		//5000-150x+x2 = 3600
		var a = [1, -150, 1400];
		equation.quadratic(a);

方程 1x^[2] + -150x + 1400 = 0 =>
Δ = b^[2] - 4ac = 16900 ;
方程的解为：x1 = 10, x2 = 140 ;
方程根与系数的关系：x1 + x2 = 150, x1 * x2 = 1400 ;

方程 3x^[2] + -8x + -10 = 0 =>
Δ = b^[2] - 4ac = 184 ;
方程的解为：x1 = -0.9274433277084227, x2 = 3.59410999437509 ;
方程根与系数的关系：x1 + x2 = 2.666666666666667, x1 * x2 = -3.333333333333334 ;

		var equation = new Equation();
		var a = [1,-8,1];
		equation.quadratic(a);
		
		var b = [2,-3,1];
		equation.quadratic(b);
		
		var c = [3,-6,4];
		equation.quadratic(c);

方程 1x^[2] + -8x + 1 = 0 =>
Δ = b^[2] - 4ac = 60 ;
方程的解为：x1 = 0.12701665379258298, x2 = 7.872983346207417 ;
方程根与系数的关系：x1 + x2 = 8, x1 * x2 = 0.9999999999999989 ;

方程 2x^[2] + -3x + 1 = 0 =>
Δ = b^[2] - 4ac = 1 ;
方程的解为：x1 = 0.5, x2 = 1 ;
方程根与系数的关系：x1 + x2 = 1.5, x1 * x2 = 0.5 ;

方程 3x^[2] + -6x + 4 = 0 =>
Δ = b^[2] - 4ac = -12 ;
没有实数解。

		var equation = new Equation();
		var a = [1,-4,-7];
		equation.quadratic(a);
		
		var b = [2,-2*Math.sqrt(2),1];
		equation.quadratic(b);
		
		var c = [5,-4,-1];
		equation.quadratic(c);
		
		var d = [1,-8,17];
		equation.quadratic(d);

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 ;

方程 2x^[2] + -2.8284271247461903x + 1 = 0 =>
Δ = b^[2] - 4ac = 1.7763568394002505e-15 ;
方程的解为：x1 = x2 = 0.7071067811865476 ;
方程根与系数的关系：x1 + x2 = 1.4142135623730951, x1 * x2 = 0.5000000000000001 ;

方程 5x^[2] + -4x + -1 = 0 =>
Δ = b^[2] - 4ac = 36 ;
方程的解为：x1 = -0.2, x2 = 1 ;
方程根与系数的关系：x1 + x2 = 0.8, x1 * x2 = -0.2 ;

方程 1x^[2] + -8x + 17 = 0 =>
Δ = b^[2] - 4ac = -4 ;
没有实数解。

		var equation = new Equation();
		var a = [1,-1,-2];
		equation.quadratic(a);
		
		var b = [4,0,-1];
		equation.quadratic(b);

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

方程 4x^[2] + 0x + -1 = 0 =>
Δ = b^[2] - 4ac = 16 ;
方程的解为：x1 = -0.5, x2 = 0.5 ;
方程根与系数的关系：x1 + x2 = 0, x1 * x2 = -0.25 ;

		var equation = new Equation();
		var a = [1,6,-15];
		equation.quadratic(a);
		
		var b = [3,7,-9];
		equation.quadratic(b);
		
		var c = [4,-5,1];
		equation.quadratic(c);

方程 1x^[2] + 6x + -15 = 0 =>
Δ = b^[2] - 4ac = 96 ;
方程的解为：x1 = -7.898979485566356, x2 = 1.8989794855663558 ;
方程根与系数的关系：x1 + x2 = -6, x1 * x2 = -14.999999999999996 ;

方程 3x^[2] + 7x + -9 = 0 =>
Δ = b^[2] - 4ac = 157 ;
方程的解为：x1 = -3.2549940143569445, x2 = 0.9216606810236113 ;
方程根与系数的关系：x1 + x2 = -2.333333333333333, x1 * x2 = -3 ;

方程 4x^[2] + -5x + 1 = 0 =>
Δ = b^[2] - 4ac = 9 ;
方程的解为：x1 = 0.25, x2 = 1 ;
方程根与系数的关系：x1 + x2 = 1.25, x1 * x2 = 0.25 ;

<span style="font-size:18px;">		var equation = new Equation();
		//(27-2x)(21-21/27*2x) = 3/4*27*21
		var a = [7/9*4, -42-42, 27*21/4];
		equation.quadratic(a);</span>

方程 3.111111111111111x^[2] + -84x + 141.75 = 0 =>
Δ = b^[2] - 4ac = 5292 ;
方程的解为：x1 = 1.808657048910078, x2 = 25.191342951089922 ;
方程根与系数的关系：x1 + x2 = 27, x1 * x2 = 45.56249999999999 ;

上下边衬1.8cm, 左右边衬1.4cm

		var equation = new Equation();
		//20*x*2+30*1.5x*2-4*1.5x2 = 1/4*20*30
		var a = [-6, 130,-150];
		equation.quadratic(a);

横条宽1.8cm, 竖条宽1.2cm

		var equation = new Equation();
		//x2 = 1-x
		var a = [1, 1, -1];
		equation.quadratic(a);

方程 1x^[2] + 1x + -1 = 0 =>
Δ = b^[2] - 4ac = 5 ;
方程的解为：x1 = -1.618033988749895, x2 = 0.6180339887498949 ;
方程根与系数的关系：x1 + x2 = -1, x1 * x2 = -1.0000000000000002 ;

		var equation = new Equation();
		//(x+1)*x/2 = 300
		var a = [0.5, 0.5, -300];
		equation.quadratic(a);

方程 0.5x^[2] + 0.5x + -300 = 0 =>
Δ = b^[2] - 4ac = 600.25 ;
方程的解为：x1 = -25, x2 = 24 ;
方程根与系数的关系：x1 + x2 = -1, x1 * x2 = -600 ;

本节到此结束，欲知后事如何，请看下回分解。