# C Program to Find All Roots of Quadratic Equation

• Write a C program to find roots of a quadratic equation.

A quadratic equation is a second order equation having a single variable. Any quadratic equation can be represented as ax2 + bx + c = 0, where a, b and c are constants( a can't be 0) and x is unknown variable.

##### For Example
2x2 + 5x + 3 = 0 is a quadratic equation where a, b and c are 2, 5 and 3 respectively.

To calculate the roots of quadratic equation we can use below formula. There are two solutions of a quadratic equation.
x = (-2a + sqrt(D))/2
x = (-2a - sqrt(D))/2

where, D is Discriminant, which differentiate the nature of the roots of quadratic equation.

Discriminant(D) value Description
D < 0 We will get two complex roots.
D = 0 We will get two equal roots.
D > 0 We will get two real numbers.

## C program to find all roots of a quadratic equation

```/*
* C Program to find square roots of a quadratic equation
*/
#include <stdio.h>
#include <conio.h>
#include <math.h>

int main() {
float a, b, c, determinant, root1, root2, real, imag;
printf("Enter coefficients a, b and c of quadratic equation ax^2 + bx + c = 0 \n");
scanf("%f%f%f", &a, &b, &c);

/* Calculate determinant */
determinant = b*b - 4*a*c;

if(determinant >= 0) {
root1= (-b + sqrt(determinant))/(2 * a);
root2= (-b - sqrt(determinant))/(2 * a);
printf("Roots of %.2fx^2 + %.2fx + %.2f = 0 are \n%.2f and %.2f",
a, b, c, root1, root2);
} else {
real= -b/(2*a);
imag = sqrt(-determinant)/(2 * a);
printf("Roots of %.2fx^2 + %.2fx + %.2f = 0 are \n%.2f+%.2fi and %.2f-%.2fi",
a, b, c, real, imag, real, imag);
}

getch();
return 0;
}
```
Program Output
```Enter coefficients a, b and c of quadratic equation ax^2 + bx + c = 0
1 1 1
Roots of 1.00x^2 + 1.00x + 1.00 = 0 are
-0.50+0.87i and -0.50-0.87i

Enter coefficients a, b and c of quadratic equation ax^2 + bx + c = 0
3 7 2
Roots of 3.00x^2 + 7.00x + 2.00 = 0 are
-0.33 and -2.00
```

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