Factoring a Quadratic

Probability Puzzles in R

Peter Chi

Assistant Professor of Statistics<br> Villanova University

What's the probability that a quadratic will factor?

$$ x^2 + 3x + 2$$

$$ x^2 + 3x + 2 = (x+2)(x+1)$$

Quadratic Equation: $ ax^2 + bx + c = 0 $

Quadratic Formula: $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

Discriminant: $ b^2 - 4ac $

Quadratic Formula: $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

Discriminant: $ b^2 - 4ac $

Example. $x^2 + 3x + 2$

if(3^2 - 4*1*2 < 0){
  return(FALSE)
}

Quadratic Formula: $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

Discriminant: $ b^2 - 4ac $

Example. $x^2 + 3x + 2$

sqrt_dscr <- sqrt(3^2 - 4*1*2)
sqrt_dscr == round(sqrt_dscr)

TRUE

is.integer does not work:

is.integer(sqrt_dscr)

FALSE

Square root is not evaluated:

value <- (-1)
if(value < 0){
  print("The value is negative.")
} else {
  print(sqrt(value))
}

"The value is negative."

Value is positive, so square root is evaluated:

value <- 4
if(value < 0){
  print("The value is negative.")
} else {
  print(sqrt(value))
}

for(i in 1:10){
  for(j in 1:10){
    print(i+j)
  }
}

Probability Puzzles in R