In this post, you will learn **how to find the roots of a quadratic equation using C** Programming language.

Quadratic Equation is any equation that can be rearranged in the standard form as ax[2] + bx = c where a,b and c are real numbers and a is not equal to 0.

The discriminant is equal to **b ^{2} – 4ac** . It tells the nature of the root.

- If the
**discriminant > 0**, then the roots are**real**. - If the
**discriminant = 0**, then the roots are**equal**. - If the
**discriminant < 0**, then the roots are**imaginary**.

Roots of the quadratic equation are obtained using these formulas.

First Root = [-b + (b^{2} – 4ac)**½] / 2a

Second Root = [-b – (b^{2} – 4ac)**½] / 2a

So, Without further ado, let’s begin the tutorial.

**C Program To Find The Roots of a Quadratic Equation**

// C Program To Find The Roots of a Quadratic Equation #include <stdio.h> #include <math.h> int main(){ float a, b, c, discriminant, root_one, root_two; // Asking for Input printf("Enter the Values of a, b and c\n"); scanf("%f %f %f", &a, &b, &c); discriminant = b * b - 4 * a * c; // logic if (discriminant > 0){ root_one = (-b + sqrt(discriminant)) / (2 * a); root_two = (-b - sqrt(discriminant)) / (2 * a); printf("The Real Roots are %f and %f", root_one, root_two); } else if (discriminant == 0){ root_one = root_two = -b / (2 * a); printf("The Equal Roots are %f", a); } else{ printf("The Roots are Imaginary"); } return 0; }

**Output**

```
Enter the Values of a, b and c
6 11 -35
The Real Roots are 1.666667 and -3.500000
```

**How Does This Program Work ?**

** float a, b, c, discriminant, root_one, root_two;
**

In this program, we have declared 6 float variable names as ** a**,

*,*

**b***,*

**c***,*

**discriminant***and*

**root_one***respectively.*

**root_two**** // Asking for Input
printf("Enter the Values of a, b and c\n");
scanf("%f %f %f", &a, &b, &c);
**

Then, the user is asked to enter the values of ** a**,

**and**

*b***.**

*c*` `**discriminant = b * b - 4 * a * c**

The discriminant of the quadratic equation is find out using **b ^{2} – 4ac**.

` `** // logic
if (discriminant > 0){
root_one = (-b + sqrt(discriminant)) / (2 * a);
root_two = (-b - sqrt(discriminant)) / (2 * a);
printf("The Real Roots are %f and %f", root_one, root_two);
}**

Now, comes the logic part of the program. If **discriminant > 0**, then roots are found using the formula stated above.

Here, the **sqrt() **function is used to find the square roots of the number.

** else if (discriminant == 0){
root_one = root_two = -b / (2 * a);
printf("The Equal Roots are %f", a);
}
**

Similarly, if **discriminant = 0**, then roots will be equal and can be found using **-b /(2 * a)** formula.

** else{
printf("The Roots are Imaginary");
}
**

And if **discriminant < 0**, then the roots will be **imaginary**.

Some of the used terms are as follows:

**#include <stdio.h>** – In the first line we have used #include, it is a preprocessor command that tells the compiler to include the contents of the stdio.h(standard input and output) file in the program.

The **stdio.h **is a file which contains input and output functions like** scanf()** and** printf()** to take input and display output respectively.

**Int main()** – Here main() is the function name and int is the return type of this function. The Execution of any Programming written in C language begins with main() function.

**scanf()** – scanf() function is used to take input from the user.

**printf()** – printf() function is used to display and print the string under the quotation to the screen.

**If. . . else **– An if statement can be followed by an optional else statement, which executes when the Boolean expression is false. If Statement executes when the Boolean expression is True.

**sqrt()** – sqrt() function is used to find the square root of a number.

**// **– Used for Commenting in C.

**Conclusion**

I hope after going through this post, you understand how to find the roots of a quadratic equation using C Programming language.

If you have any doubt regarding the topic, feel free to contact us in the Comment Section. We will be delighted to help you.