In WillJordan95/WillQuadratic: Finds roots of a given quadratic

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Loading the package

library(WillQuadratic)

This package contains a function, quadratic_formula(), that can be used to find roots of a quadratic for given coefficients. It also contains a dataset, 'Pokemon'. This dataset containts summary statistics for Pokemon, generations 1-6. This dataset was found on Kaggle. More information can be found on this dataset here.

Using the quadratic_formula() function

The quadratic_formula() function finds the roots of a quadratic in the form

$$ ax^2 + bx + c = 0 $$ by taking the coefficients (a,b,c) as inputs and applying the quadratic formula

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

If the quadratic has one repeated root, the function returns a numeric with that value. If the quadratic has distint, real roots, the function returns a vector of numerics containing the solutions. If the quadratic has non-real roots, the vector of solutions contains objects of class complex.

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Example 1 - Repeated root

Consider the quadratic

$$ x^2 - 10x + 25 = 0 $$ That is, (a=1,b=-10,c=25), we would expect

$$ \begin{aligned} x = \frac{10 \pm \sqrt{(-10)^2 - 4(25)}}{2} \[1em] = \frac{10 \pm \sqrt{100 - 100}}{2} \[1em] = 5 \end{aligned} $$ Hence, using quadratic_formula() we have

quadratic_formula(1, -10, 25)

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Example 2 - Distinct, real roots

Consider the quadratic

$$ 2x^2 - 10x + 12 = 0 $$ That is, (a=2, b=-10, c=12), we would expect

$$ \begin{aligned} x = \frac{10 \pm \sqrt{(-10)^2 - 4(2)(12)}}{2(2)} \[1em] = \frac{10 \pm \sqrt{100 - 96}}{4} \[1em] = \frac{10 \pm 2}{4} \[1em] = 2,3 \end{aligned} $$ Hence, using quadratic_formula() we have

quadratic_formula(2, -10, 12)

Example 3 - Non-real roots

Consider the quadratic

$$ x^2 - 2x + 2 = 0 $$ That is, (a=1, b=-2, c=2), we would expect

$$ \begin{aligned} x = \frac{2 \pm \sqrt{(-2)^2 - 4(2)}}{2} \[1em] = \frac{2 \pm \sqrt{4 - 8}}{2} \[1em] = \frac{2 \pm \sqrt{-4}}{2} \[1em] = 1 \pm \sqrt{-1} \[1em] = 1 + i, 1-i \end{aligned} $$ Hence, using quadratic_formula() we have

x <- quadratic_formula(1, -2, 2)
x
class(x)

WillJordan95/WillQuadratic documentation built on June 7, 2019, 2:34 p.m.