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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: ")
coefficients <- as.numeric(unlist(strsplit(readLines(n=1), " ")))
# Assigning individual coefficients to variables a, b, and c
a <- coefficients[1]
b <- coefficients[2]
c <- coefficients[3]
# 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.
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