# C++ Program to Solve Quadratic Equations

The C++ program to solve quadratic equations in standard form is a simple program based on the quadratic formula. Given the coefficients as input it will solve the equation and output the roots of the equation.

This is a simple program is intended for intermediate level C++ programmers.

The program is compiled using Dev-C++ 4.9.9.2 version installed on a Windows 7 64-bit PC. You may try other standard C compilers and the program will still work if you use the correct C libraries.

## Problem Definition

In this program, we solve the quadratic equation using the formula

$\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\ \end{array}$

Where a, b and c are coefficient of the equation ax^2 + bx + c = 0 which is in the standard form.

How to compute?

The steps to compute quadratic equation is given below.

Step1:

The program request the input coefficient values a, b and c. When the user input the values, it will compute two terms t1 and t3 and an intermediate term t2.

t1 = -1 * b

Step2:

The function term2 () is called in step 2 and returned value of function is assigned to t2. The term2 () function receives the coefficient values – a, b, c and compute the value for t2.

t2 = term2(a, b, c);

The term () function returns and assign value of b2 – 4ac to t2 and it is useful in understanding the root of the quadratic equation.

For example,

If (t2 < 0), then the roots are not real

If (t2 == 0) then, there is exactly one root value.

If (t2 > 0) then there are two root values.

The above condition is checked and printed with output values. Now we need to compute the roots and display the output values.

Step3:

A term t3 is assigned value after taking square root of t2.

t3 = sqrt (t2);

Step4:

Finally, we have t1 and t3 to compute two roots of a quadratic equation.

root1 = (t1 + t3)/ 2 * a;

root2 = (t1 + t3)/ 2 * a;

Then root1 and root are calculated and printed immediately.

## Flowchart – Program for Quadratic Equations

To understand flow of logic of this program, see the flowchart below.

## Program Code – Program for Quadratic Equation

/* C Program to solve a quadratic equation - Ax^2 + Bx + C = 0 using the formula

X1= -b + sqrt (b^2 – 4 * a * c)/ (2 * a) and X2 = -b - sqrt (b^2 – 4 * a * c)/ (2* a) */

#include <cstdlib>

#include <conio.h>

#include <iostream>

#include <cmath>

using namespace std;

int main ()

{

int term2 (int a, int b, int c);

/* coefficients a, b, c */

int a, b, c;

float root1, root2, t1, t2, t3;

root1 = root2 = 0.0;

cout << "\n\n\n\n\n\n";

cout << "\t\t\t\tPlease enter coefficients:" << endl;

cout << "\t\t\t\tA=";

cin >> a;

cout << "\t\t\t\tB=";

cin >> b;

cout << "\t\t\t\tC=";

cin >> c;

cout << "\t\t\t\tA=" << " " << a;

cout << "\tB=" << " " << b;

cout << "\tC=" << " " << c << endl;

cout << endl;

t1 = -1 * b;

t2 = term2 (a, b, c);

t3 = sqrt (t2);

root1 = (t1 + t3)/ (2 * a);

root2 = (t1 - t3)/ (2 * a);

cout << "\t\t\t\tRoot-1 =" << " " << root1 << endl;

cout << "\t\t\t\tRoot-2 =" << " " << root2 << endl;

getch ();

return EXIT_SUCCESS;

}

int term2 (int x, int y, int z)

{

int p = y * y;

int q = 4 * x * z;

int r = p - q;

if (r < 0)

cout << "\t\t\t\tThere is no real root." << endl;

if (r == 0)

cout << "\t\t\t\tThere is only one real root." << endl;

if (r > 0)

cout << "\t\t\t\tThere are two real roots." << endl;

return r;

}

## Output

The output of the above program is given below.