R Program - Find Roots of a Quadratic Equation

A standard form of a quadratic equation is:

ax² + bx + c = 0

Where:

a, b and c are real numbers and a ≠ 0.

Roots of the equation are:

For Example:

The roots of equation x² + 5x + 4 = 0 is

The roots of the equation will be imaginary if D = b² - 4ac < 0. For example - the roots of equation x² + 4x + 5 = 0 will be

Example: Calculate roots of a Quadratic equation

In the example below, a function called roots is created which takes a, b and c as arguments to calculate the roots of the equation ax² + bx + c = 0.

roots <- function(a, b, c) {
  D <- b*b - 4*a*c
  if (D >= 0) {
    x1 <- (-b + sqrt(D))/(2*a)
    x2 <- (-b - sqrt(D))/(2*a)
    cat("Roots are:", x1,",",x2,"\n")    
  } else {
    x1 <- -b/(2*a)
    x2 <- sqrt(-D)/(2*a)
    cat("Roots are:", x1,"±",x2,"i\n")      
  }
}

cat("Equation is x*x+5x+4=0 \n")
roots(1,5,4)
cat("\nEquation is x*x+4x+5=0 \n")
roots(1,4,5)

The above code will give the following output:

Equation is x*x+5x+4=0 
Roots are: -1 , -4 

Equation is x*x+4x+5=0 
Roots are: -2 ± 1 i