Week 1 Homework

1. Write a loop that calculates 12-factorial

Factorial <- 1

for(i in 1:12)
{
  Factorial <- Factorial * i
}

2. Show how to create a numeric vector that contains the sequence from 20 to 50 by 5.

NumVector <- seq(from = 20, to = 50, by = 5)
NumVector

## [1] 20 25 30 35 40 45 50

NumVector2 <- seq(20, 50, 5)
NumVector2

## [1] 20 25 30 35 40 45 50

3. Create the function “quadratic” that takes a trio of input numbers a, b, and c and solve the quadratic equation. The function should print as output the two solutions.

quadratic <- function (a,b,c)
{
  if(a == 0)
  {
    return ("Cannot be computed")
  }
  
  else if (is.na (sqrt(b^2 - 4*a*c) < 0 ))
  {
    return ("There are no real roots")
  }
  
  else if (sqrt(b^2 - 4*a*c) == 0)
  {
    Sol <- (-b / 2*a)
    return (sprintf("Solution is %s",Sol))
  }
  
  else
  {
    Sol1 <- (-b + sqrt(b^2 - 4*a*c)) / (2*a) 
      
    Sol2 <- (-b - sqrt(b^2 - 4*a*c)) / (2*a) 
    
    return (sprintf("Solutions are %s, and %s", 
                    format(round(Sol1,8), nsmall = 8), 
                    format(round(Sol2,8), nsmall = 8)))
  }
  
}

#Test Runs
quadratic(1,0,5)

## Warning in sqrt(b^2 - 4 * a * c): NaNs produced

## [1] "There are no real roots"

quadratic(0,1,5)

## [1] "Cannot be computed"

quadratic(2,4,2)

## [1] "Solution is -4"

quadratic(1,7,5)

## [1] "Solutions are -0.80741760, and -6.19258240"