Quadratic Root in R Solve Calculator

How to Use This Calculator

To solve a quadratic equation of the form ax² + bx + c = 0, follow these steps:

1. Enter the coefficients a, b, and c in the calculator form
2. Click "Calculate" to find the roots
3. View the results and R implementation code
4. Copy the R code to your project if needed

The Quadratic Formula

The quadratic formula is the standard method for solving quadratic equations:

Where:

• a, b, c are coefficients of the quadratic equation
• √(b² - 4ac) is the discriminant
• The ± symbol indicates there are two possible solutions

The discriminant determines the nature of the roots:

• If discriminant > 0: Two distinct real roots
• If discriminant = 0: One real root (repeated)
• If discriminant < 0: Two complex roots

Implementing in R

To solve quadratic equations in R, you can use the quadratic formula directly or use built-in functions. Here's a basic implementation:

# Basic quadratic solver in R
quadratic_solver <- function(a, b, c) {
  discriminant <- b^2 - 4*a*c
  if (discriminant > 0) {
    root1 <- (-b + sqrt(discriminant))/(2*a)
    root2 <- (-b - sqrt(discriminant))/(2*a)
    return(list(roots = c(root1, root2), type = "real"))
  } else if (discriminant == 0) {
    root <- -b/(2*a)
    return(list(roots = root, type = "repeated"))
  } else {
    real_part <- -b/(2*a)
    imag_part <- sqrt(-discriminant)/(2*a)
    root1 <- complex(real = real_part, imaginary = imag_part)
    root2 <- complex(real = real_part, imaginary = -imag_part)
    return(list(roots = c(root1, root2), type = "complex"))
  }
}

This function handles all cases of quadratic equations and returns the roots along with their type.

Worked Example

Let's solve the equation x² - 5x + 6 = 0:

1. Identify coefficients: a = 1, b = -5, c = 6
2. Calculate discriminant: (-5)² - 4(1)(6) = 25 - 24 = 1
3. Since discriminant > 0, there are two real roots
4. Apply quadratic formula:
   • x₁ = [5 + √1]/2 = 3
   • x₂ = [5 - √1]/2 = 2

The roots are 3 and 2.

Interpreting Results

When using this calculator, pay attention to:

• The nature of the roots (real, repeated, or complex)
• The discriminant value which indicates the number of solutions
• The R implementation code which you can adapt for your projects

For real roots, you can use the values directly in your calculations. For complex roots, you may need to consider their real and imaginary components separately.