C Program to Find Roots of Quadratic Equation

Definition of Quadratic Equations in Programming

In programming, a quadratic equation is generally represented in the form \[ax^2 + bx + c = 0\]where a, b, and c are constants. The term x represents the variable of the equation. In this context, a cannot equal zero, because if it did, the equation would be linear instead of quadratic.To solve this equation and find its roots, the quadratic formula is utilized:\[x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\]This formula provides two possible solutions for x in a quadratic equation, which correspond to the values at which the function crosses the horizontal axis.

C Program to Find Roots of Quadratic Equation Using Functions

When solving a quadratic equation using C programming, implementing functions can help organize your code efficiently. It not only makes your program readable but also reusable.

Example of Solving Quadratic Equations in C

Below is an example of a C program that finds the roots of a quadratic equation using functions. The equation is expressed as \[ax^2 + bx + c = 0\].Here's a step-by-step breakdown of the code using functions to manage the complexity:

• Step 1: Declare a function to calculate the discriminant \[D\], which is \[b^2 - 4ac\].
• Step 2: Create another function to compute the roots using the quadratic formula \[x = \frac{-b \pm \sqrt{D}}{2a}\].
• Step 3: In the main function, take inputs for \(a\), \(b\), and \(c\), and call the above functions.
• Step 4: Display the results according to the discriminant value.

C Program to Find Imaginary Roots of Quadratic Equation

Identifying the imaginary roots of a quadratic equation is a key aspect of computational mathematics using C programming. Imaginary roots occur when the discriminant of the quadratic equation\[b^2 - 4ac\] is negative, indicating that there are no real number solutions.

C Program to Find Real Roots of Quadratic Equation

To find the real roots of a quadratic equation using C programming, focus on understanding when the roots are real and how to calculate them using the quadratic formula. Real roots occur when the discriminant \(b^2 - 4ac\) is zero or positive.

C Program to Find Roots of Quadratic Equation Using If

In C programming, using conditional if statements is a straightforward way to determine the nature of the roots of a quadratic equation. Depending on the discriminant value, the program can branch into computing real and distinct roots, a double root, or complex roots.

Implementation of Conditional Statements in C

The method uses if-else conditions to evaluate the discriminant \(b^2 - 4ac\). Let's explore this through an example program.Consider the quadratic equation \[ax^2 + bx + c = 0\]. The steps to solve the equation using if statements are as follows:

• Step 1: Calculate the discriminant \(D = b^2 - 4ac\).
• Step 2: Use the if statement to determine whether \(D\) is positive, zero, or negative.
• Step 3: Based on the value of the discriminant, compute the roots accordingly:

 ' if (D > 0) {    x1 = (-b + sqrt(D)) / (2*a);    x2 = (-b - sqrt(D)) / (2*a); } '

'else if (D == 0) {    x1 = x2 = -b / (2*a); } '

' else {    realPart = -b / (2*a);    imaginaryPart = sqrt(-D) / (2*a); } '