R Bridge: Week 1 Assignment

Question 1

Write a loop that calculates 12 factorial

ans_1 = 1
for (j in 1:12)
    ans_1 <- ans_1 * j
ans_1

## [1] 479001600

Question 2

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

• Option A

ans_2a <- 5 * 4:10
ans_2a

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

• Option B

ans_2b <- seq(20, 50, 5)
ans_2b

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

Question 3

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

# This function solves for the roots of the quadratic equation specified
# by the coefficients a, b and c, which are assumed to be real numbers:
#   ax^2 + bx + c = 0
# The function handles several special cases:
#   - a = 0: linear equation, so only 1 root 
#   - b^2 = 4ac: only 1 root 
#   - b^2 < 4ac: no real roots (only complex roots)

factorial <- function(a,b,c) {
    if (a == 0)
        paste("a=0, not a quadratic equation, only 1 root: ", - c / b)
    else {
        disc <- b ^ 2 - 4 * a * c       # calc the discriminant
        term1 <- - b / 2 / a            # calc first term
        if (disc == 0)
            paste("b^2 = 4ac, only 1 root: ", term1)
        else {
            if (disc < 0)
                paste("b^2 < 4ac, no real solution")
            else {
                term2 <- sqrt(disc) / 2 / a     # calc second term
                paste("2 real roots: ", term1 + term2, " and ", term1 - term2)
            }
        }
    }
}

# Now try some examples

factorial(0, -2, 1)

## [1] "a=0, not a quadratic equation, only 1 root:  0.5"

factorial(1, -6, 9)

## [1] "b^2 = 4ac, only 1 root:  3"

factorial(1, 1, 1)

## [1] "b^2 < 4ac, no real solution"

factorial(2, 5, -3)

## [1] "2 real roots:  0.5  and  -3"

factorial(5, pi, -2)

## [1] "2 real roots:  0.392024877772891  and  -1.02034340849085"