# 1. Introduction

In this tutorial, we will develop an R program to compute and display the roots of a quadratic equation.

# 2. Program Overview

The program will:

1. Prompt the user to input the values for coefficients ( a ), ( b ), and ( c ).

2. Calculate the discriminant.

3. Determine the nature of the roots based on the value of the discriminant.

4. Calculate and display the roots accordingly.

# 3. Code Program

``````# Prompt the user to input the coefficients of the quadratic equation
cat("Enter the coefficients a, b, and c separated by spaces: ")

# Assigning individual coefficients to variables a, b, and c
a <- coefficients
b <- coefficients
c <- coefficients

# Calculate the discriminant
delta <- b^2 - 4*a*c

# Check the nature of the roots based on the discriminant and calculate the roots
if(delta > 0) {
root1 <- (-b + sqrt(delta)) / (2*a)
root2 <- (-b - sqrt(delta)) / (2*a)
cat("The equation has two distinct real roots:", root1, "and", root2, "\n")
} else if(delta == 0) {
root1 <- -b / (2*a)
cat("The equation has one real repeated root:", root1, "\n")
} else {
realPart <- -b / (2*a)
imaginaryPart <- sqrt(abs(delta)) / (2*a)
cat("The equation has complex roots:", realPart, "+", imaginaryPart, "i and", realPart, "-", imaginaryPart, "i\n")
}
``````

### Output:

```Enter the coefficients a, b, and c separated by spaces: 1 -3 2
The equation has two distinct real roots: 2 and 1
```

# 4. Step By Step Explanation

1. The program commences by prompting the user to input the coefficients ( a ), ( b ), and ( c ) using the cat function.

2. The coefficients are captured as a string, split based on spaces, and converted to numeric format. They are then assigned to individual variables for ease of computation.

3. The discriminant ((Delta)) is computed using the formula ( b^2 - 4ac ).

4. The nature of the roots is then determined based on the value of the discriminant:

- If ( Delta > 0 ), the equation has two distinct real roots.- If ( Delta = 0 ), the equation has a single real repeated root.- If ( Delta < 0 ), the equation has complex conjugate roots.

5. Using appropriate formulas, the roots are computed and displayed to the user using the cat function.