This program will solve quadratic equations. It accepts coefficients of a quadratic equation from the user i.e. a, b and c and displays the roots.
To compile the program name it quadratic_solver.cpp then type
g++ -o quadratic_solver quadratic_solver.cpp
You may need to use math.h like this: #include if you are using C++ compiler software on Windows. (I tried it without the <math.h>and got an “undeclared identifier” error)
What is Quadratic Equation?
The Quadratic equation is the equation of the form as below:
ax2 + bx +c = 0
Where x represents unknown and a, b and c are coefficients, it’s roots is given by following the formula.
Quadratic Equation – C++ Implementation
Here,
The term b2-4ac is known as the discriminant of a quadratic equation. The discriminant tells the nature of the roots.
- If discriminant is greater than 0, the roots are real and different.
- If discriminant is equal to 0, the roots are real and equal.
- If discriminant is less than 0, the roots are complex and different.
C++ Program to Solve Quadratic Equation
/*
program to find solution to quadratic equation in the standard form ax^+bx+c=0.
Author David Tarsi. The logic portion of this program was developed from instruction.
The coding is by the author. Any questions or comments welcome
at dtarsi@premier1.net
*/
#include <iostream>
#include <math.h>
using namespace std;
void one()
{
float a = 0.0; //here we declare the variables and use float because we
float b = 0.0; //are dealing with square roots
float c = 0.0;
float x1 = 0.0;
float x2 = 0.0;
float x3 = 0.0;
float x4 = 0.0;
//this section gets user input and displays message
cout << "Enter the coefficients a , b , c for equation in the form ax^ + bx + c = 0:\n";
cout << "Enter value for a:\n";
cin >> a;
cout << "Enter value for b:\n";
cin >> b;
cout << "Enter value for c:\n";
cin >> c;
//are all the coefficients 0? if so both roots are 0
if (a == 0 && b == 0 && c == 0) {
x1 = 0;
x2 = 0;
cout << "The roots are:"
"\n"
<< "x1 = " << x1 << " , "
<< "x2 = " << x2 << "\n";
}
//is c the only non-zero number? if so tell the user
if (a == 0 && b == 0 && c != 0) {
c = c;
cout << "There are no roots"
"\n"
<< "c = " << c << "\n";
}
//is a zero? if so solve the resulting linear equations and notify user
if (a == 0 && b != 0 && c != 0) {
cout << "The values entered do not make a quadratic expression"
"\n"
<< "x = " << -c / b << "\n";
}
//if b is zero and c is zero tell user
if (a == 0 && b != 0 && c == 0) {
x1 = 0;
x2 = 0;
cout << "The roots are:"
"\n"
<< "x1 = " << x1 << " , "
<< "x2 = " << x2 << "\n";
}
//if b and c are equal to zero then ax^=0 and since a cannot be zero without x being
// zero also let user know
if (a != 0 && b == 0 && c == 0) {
x1 = 0;
x2 = 0;
cout << "The values entered result in ax^= 0; so both roots are 0"
"\n"
<< "x1 = " << x1 << " , "
<< "x2 = " << x2 << "\n";
}
//factor out x from ax^+bx=0 and either x = 0 or ax + b =0
//then solve the linear equation
if (a != 0 && b != 0 && c == 0) {
x1 = 0;
x2 = -b / a;
cout << "The roots are:"
"\n"
<< "x1 = " << x1 << " , "
<< "x2 = " << x2 << "\n";
}
//now we get to use the square root function and let the user
//know they have some imaginary numbers to deal with
if (a < 0 && b == 0 && c < 0) {
x1 = -b / (2 * a);
x4 = (b * b) - (4 * a * c);
x4 = -x4;
x2 = sqrt(x4) / (2 * a);
x3 = -sqrt(x4) / (2 * a);
cout << "The roots are not real numbers:"
"\n"
<< "x1 =" << x1 << " + " << x2 << " * i "
<< "\n"
<< "x2 =" << x1 << " + " << x3 << " * i "
<< "\n";
}
if (a > 0 && b == 0 && c > 0) {
x1 = -b / (2 * a);
x4 = (b * b) - (4 * a * c);
x4 = -x4;
x2 = sqrt(x4) / (2 * a);
x3 = -sqrt(x4) / (2 * a);
cout << "The roots are not real numbers:"
"\n"
<< "x1 =" << x1 << " + " << x2 << " * i "
<< "\n"
<< "x2 =" << x1 << " + " << x3 << " * i "
<< "\n";
}
//now a and c are opposite signs so the answer will be real
if (a > 0 && b == 0 && c < 0) {
x1 = (-b + (sqrt(pow(b, 2) - (4 * a * c)))) / (2 * a);
x2 = (-b - (sqrt(pow(b, 2) - (4 * a * c)))) / (2 * a);
cout << "The roots are:"
"\n"
<< "x1 = " << x1 << " , "
<< "x2 = " << x2 << "\n";
}
if (a < 0 && b == 0 && c > 0) {
x1 = (-b + (sqrt(pow(b, 2) - (4 * a * c)))) / (2 * a);
x2 = (-b - (sqrt(pow(b, 2) - (4 * a * c)))) / (2 * a);
cout << "The roots are:"
"\n"
<< "x1 = " << x1 << " , "
<< "x2 = " << x2 << "\n";
}
//ok now if we end up not having to take the square root of a neg
// do the math
if (a != 0 && b != 0 && c != 0 && (4 * a * c) <= pow(b, 2)) {
x1 = (-b + (sqrt(pow(b, 2) - (4 * a * c)))) / (2 * a);
x2 = (-b - (sqrt(pow(b, 2) - (4 * a * c)))) / (2 * a);
cout << "The roots are:"
"\n"
<< "x1 = " << x1 << " , "
<< "x2 = " << x2 << "\n";
}
//here we have to deal with non x intercepts ie: sqrt(-1)
// alter the formula slightly to give correct output and
// let the user know
if (a != 0 && b != 0 && c != 0 && (4 * a * c) > pow(b, 2)) {
x1 = -b / (2 * a);
x4 = (b * b) - (4 * a * c);
x4 = -x4;
x2 = sqrt(x4) / (2 * a);
x3 = -sqrt(x4) / (2 * a);
cout << "The roots are not real numbers"
"\n"
<< "x1 =" << x1 << " + " << x2 << " * i "
<< "\n"
<< "x2 =" << x1 << " + " << x3 << " * i "
<< "\n";
}
return;
}
//keep output from vanishing before we can read it.
void two()
{
char c;
cout << "Press c and then Enter to continue...."
"\n";
cin >> c;
for (;;) {
if (c) {
break;
}
}
cout << "Done"
"\n";
}
int main()
{
one();
two();
return 0;
}Output of C++ Program
Compile: $ g++ -o quadratic_solver quadratic_solver.cpp
Run:
$ ./quadratic_solver
Enter the coefficients a , b , c for equation in the form ax^ + bx + c = 0:
Enter value for a:
6
Enter value for b:
4
Enter value for c:
1
The roots are not real numbers
x1 =-0.333333 + 0.235702 * i
x2 =-0.333333 + -0.235702 * i
$ ./quadratic_solver
Enter the coefficients a , b , c for equation in the form ax^ + bx + c = 0:
Enter value for a:
9
Enter value for b:
24
Enter value for c:
2
The roots are:
x1 = -0.0861142 , x2 = -2.58055