R1

1. t_factorial <- 1 for (i in 1:12) { t_factorial <- t_factorial * i } print(t_factorial)
2. numVec<-seq(20, 50, by=5) numVec

3. Factorial <- function (a, b, c) { Discriminant <- b ^ 2 - 4 * a * c # Find the Discriminant if (Discriminant >= 0) { Sol1 <- (-b + sqrt(Discriminant)) / 2 * a # Find First Solution Sol2 <- (-b - sqrt(Discriminant)) / 2 * a # Find Second Solution } else # Working Imaginary Solutions { print(" THE SOLUTION TO THIS EQUATION IS IN THE COMPLEX GROUP OF NUMBERS “) Sol1 <- paste(”(“,-b ,”+“, sqrt(-Discriminant),”i)“,”/(“, 2 * a,”)“) # Imaginary Solutions Sol2 <- paste(”(“,-b ,”-“, sqrt(-Discriminant),”i)“,”/(“, 2 * a,”)“) # Imaginary Solutions if (b == 0) # Simplifying Fractions { Sol1 <- paste(sqrt(-Discriminant),”i/(“, 2 * a,”)“) # Imaginary Solutions Sol2 <- paste(-sqrt(-Discriminant),”i/(“, 2 * a,”)“) # Imaginary Solutions if (sqrt(-Discriminant) == a) { Sol1 <- paste(”i“,”/“, 2) # Imaginary Solutions Sol2 <- paste(”-i“,”/“, 2) # Imaginary Solutions if (sqrt(-Discriminant) == 2) { Sol1 <- paste(”i“) # Imaginary Solutions Sol2 <- paste(”-i“) # Imaginary Solutions } } if (sqrt(-Discriminant) == 2) { Sol1 <- paste(”i“,”/“, a) # Imaginary Solutions Sol2 <- paste(”-i“,”/“, a) # Imaginary Solutions if (a == 1) { Sol1 <- paste(”i“) # Imaginary Solutions Sol2 <- paste(”-i“) # Imaginary Solutions } } } } if (b >= 0) { b = paste(”+“,b) } if (c >= 0) { c = paste(”+“,c) } # Final Print outs OriginalEquation <- paste(a,”x^2“,b,”x“,c,”= 0“) print(paste(”The original Equation is: “, OriginalEquation)) print(paste(”The first solution is: x1 = “, Sol1)) print(paste(”The second solution is: x2 = “, Sol2)) if (is.numeric(Sol1) & is.numeric(Sol2)) { Equation <- paste(”(x +“, (-1 * Sol1),”)(x +", (-1 *Sol2), “) = 0”)

   if (Sol1 == Sol2) { Equation <- paste(“(x”, -1 * Sol1, “)^2 = 0”) } } else { Equation <- paste(“(x +”, ( Sol1), “)(x +”, ( Sol2), “) = 0”)

   if (Sol1 == Sol2) { Equation <- paste(“(x”, Sol1, “)^2 = 0”) } } print(paste(“The factorized equation will be:”, Equation)) # SolutionsFrame <- data.frame(“Original” = OriginalEquation, “x1” = Sol2, “x2” = Sol1, “Equation” = Equation) # SolutionsFrame }

Factorial(7,17,10)