判别式为负时二次returns错虚解的解法

Question

我正在尝试更多地参与编程，这是朋友推荐我做的一件事。我正在尝试编写一个二次求解器，但它给出了错误的答案，但是我们都不知道为什么。

我们以这个等式为例：x^2+4x+5 = 0
它的解是 x=-2+1 和 x=-2-i
Eclipse 控制台显示如下：

Quadratic equation: 
Please enter A: 
1
Please enter B: 
4
Please enter C: 
5
Your first solution is: -3.0
Your second solution is: -5.0

这是正在使用的代码：

import java.util.Scanner;

public class Main{

    private static Scanner input = new Scanner(System.in);

    public static void main(String[] args) {

        System.out.println("Quadratic equation: ");
        System.out.println("Please enter A: ");

        while(!input.hasNextInt()){
            @SuppressWarnings("unused")
            String broken = input.next();
            System.out.println("Please enter A: ");
        }

        int a = input.nextInt();
        System.out.println("Please enter B: ");

        while(!input.hasNextInt()){
            @SuppressWarnings("unused")
            String broken = input.next();
            System.out.println("Please enter B: ");
        }

        int b = input.nextInt();
        System.out.println("Please enter C: ");

        while(!input.hasNextInt()){
            @SuppressWarnings("unused")
            String broken = input.next();
            System.out.println("Please enter C: ");
        }

        int c = input.nextInt();

        double imaginaryCheck = (b*b)-(4*a*c);

        if(imaginaryCheck>0){
            double plus = (-b) + Math.sqrt(imaginaryCheck) / (2 * a);
            double minus = (-b) - Math.sqrt(imaginaryCheck) / (2 * a);
            System.out.format("Your first solution is: %1.2f\n", plus);
            System.out.format("Your second solution is: %1.2f", minus); 
        }else{
            double plus = (-b) + Math.sqrt((-1*imaginaryCheck)) / (2 * a);
            double minus = (-b) - Math.sqrt((-1*imaginaryCheck)) / (2 * a);
            System.out.format("Your first solution is: %1.2fi\n", plus);
            System.out.format("Your second solution is: %1.2fi", minus); 
        }
    }
}

是哪里出错了还是我搞错了方程式？

Answer 1

您可能应该为 imaginaryCheck==0 添加一个案例，因为在那种情况下您只能得到一个解决方案。
你总是忘记分数部分的括号导致你使用的实际公式错误
最大的问题：你的假想解计算有误。这不是虚数值的计算方式。

正确的应该是这样的：

double plusReal = (-b) / (double)(2 * a);
double minusReal = (-b) / (double)(2 * a);

double plusImaginary = Math.sqrt(-1 * imaginaryCheck) / (2 * a);
double minusImaginary = -Math.sqrt(-1 * imaginaryCheck) / (2 * a);

System.out.format("Your first solution is: %1.2f + %1.2fi\n", plusReal, plusImaginary);
System.out.format("Your second solution is: %1.2f + %1.2fi", minusReal, minusImaginary);

你必须分别计算实部和虚部——你不能简单地将它们相加。这将正确输出：

Your first solution is: -2.00 + 1.00i
Your second solution is: -2.00 + -1.00i

if-分支应如下所示，并带有更正的括号：

double plus = ((-b) + Math.sqrt(imaginaryCheck)) / (2 * a);
double minus = ((-b) - Math.sqrt(imaginaryCheck)) / (2 * a);
System.out.format("Your first solution is: %1.2f\n", plus);
System.out.format("Your second solution is: %1.2f", minus);

代码最终应该看起来像

if (imaginaryCheck > 0) {
    double plus = (-b + Math.sqrt(imaginaryCheck)) / (2 * a);
    double minus = (-b - Math.sqrt(imaginaryCheck)) / (2 * a);

    System.out.format("Your first solution is: %1.2f\n", plus);
    System.out.format("Your second solution is: %1.2f", minus);
} else if (imaginaryCheck == 0) {
    double plus = -b / (double) (2 * a);

    System.out.format("Your only solution is: %1.2f\n", plus);
} else {
    double plusReal = -b / (double) (2 * a);
    double plusImaginary = Math.sqrt(-1 * imaginaryCheck) / (2 * a);

    System.out.format("Your first solution is: %1.2f + %1.2fi\n", plusReal, plusImaginary);
    System.out.format("Your second solution is: %1.2f - %1.2fi", plusReal, plusImaginary);
}

Answer 2

您需要将计算更改为：

    if(imaginaryCheck>0){
        double plus = ((-b) + Math.sqrt(imaginaryCheck)) / (2 * a);
        double minus = ((-b) - Math.sqrt(imaginaryCheck)) / (2 * a);
        System.out.format("Your first solution is: %1.2f\n", plus);
        System.out.format("Your second solution is: %1.2f", minus); 
    }else{
        double plus = ((-b) + Math.sqrt((-1*imaginaryCheck))) / (2 * a);
        double minus = ((-b) - Math.sqrt((-1*imaginaryCheck))) / (2 * a);
        System.out.format("Your first solution is: %1.2fi\n", plus);
        System.out.format("Your second solution is: %1.2fi", minus); 
    }

原因：因为*和/运算符的优先级高于+和-。详情请参考link

假设：您计算的虚部是正确的，即 %1.2fi。如果不确定计算本身，那么 luk2302 求虚解的解就可以了。

判别式为负时二次returns错虚解的解法

Solution for quadratic returns wrong imaginary solutions when the discriminant is negative

java

math

quadratic