Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
C++ Program to Find All Roots of a Quadratic Equation
A quadratic equation is in the form ax2 + bx + c. The roots of the quadratic equation are given by the following formula −
There are three cases −
b2 < 4*a*c - The roots are not real i.e. they are complex
b2 = 4*a*c - The roots are real and both roots are the same.
b2 > 4*a*c - The roots are real and both roots are different
The program to find the roots of a quadratic equation is given as follows.
Example
#include<iostream>
#include<cmath>
using namespace std;
int main() {
int a = 1, b = 2, c = 1;
float discriminant, realPart, imaginaryPart, x1, x2;
if (a == 0) {
cout << "This is not a quadratic equation";
}else {
discriminant = b*b - 4*a*c;
if (discriminant > 0) {
x1 = (-b + sqrt(discriminant)) / (2*a);
x2 = (-b - sqrt(discriminant)) / (2*a);
cout << "Roots are real and different." << endl;
cout << "Root 1 = " << x1 << endl;
cout << "Root 2 = " << x2 << endl;
} else if (discriminant == 0) {
cout << "Roots are real and same." << endl;
x1 = (-b + sqrt(discriminant)) / (2*a);
cout << "Root 1 = Root 2 =" << x1 << endl;
}else {
realPart = (float) -b/(2*a);
imaginaryPart =sqrt(-discriminant)/(2*a);
cout << "Roots are complex and different." << endl;
cout << "Root 1 = " << realPart << " + " << imaginaryPart << "i" <<end;
cout << "Root 2 = " << realPart << " - " << imaginaryPart << "i" <<end;
}
}
return 0;
}Output
Roots are real and same. Root 1 = Root 2 =-1
In the above program, first the discriminant is calculated. If it is greater than 0, then both the roots are real and different.
This is demonstrated by the following code snippet.
if (discriminant > 0) {
x1 = (-b + sqrt(discriminant)) / (2*a);
x2 = (-b - sqrt(discriminant)) / (2*a);
cout << "Roots are real and different." << endl;
cout << "Root 1 = " << x1 << endl;
cout << "Root 2 = " << x2 << endl;
}If the discriminant is equal to 0, then both the roots are real and same. This is demonstrated by the following code snippet.
else if (discriminant == 0) {
cout << "Roots are real and same." << endl;
x1 = (-b + sqrt(discriminant)) / (2*a);
cout << "Root 1 = Root 2 =" << x1 << endl;
}If the discriminant is less than 0, then both the roots are complex and different. This is demonstrated by the following code snippet.
else {
realPart = (float) -b/(2*a);
imaginaryPart =sqrt(-discriminant)/(2*a);
cout << "Roots are complex and different." << endl;
cout << "Root 1 = " << realPart << " + " << imaginaryPart << "i" << endl;
cout << "Root 2 = " << realPart << " - " << imaginaryPart << "i" << endl;
}
7K+ Views
