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:

`ax`

^{2} + bx +c = 0

Where x represents unknown and a, b and c are coefficients, it’s roots is given by following the formula.

Here,

The term `b`

is known as the discriminant of a quadratic equation. The discriminant tells the nature of the roots.^{2}-4ac

- 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