Roots of a quadratic function: Difference between revisions

=={{header|Nim}}==

<lang nim>import complex

import math

import strformat

func quadRoots(a, b, c: float): array[2, Complex[float]] =

var (a, b, c) = (a, b, c)

b /= a

c /= a

var Δ = b ^ 2 - 4 * a * c

if Δ == 0.0:

return [complex(-c / b), complex(0.0)]

var d = sqrt(complex(Δ))

if b < 0.0:

d -= complex(b)

return [d / complex(2.0 * a), complex(2.0 * c) / d]

else:

d = -d - b

return [complex(2 * c) / d, d / complex(2 * a)]

var a = [2.0, 1.0, 1.0, 10.0]

var b = [10.0, 2.0, -10.0 ^ 9, 1]

var c = [1.0, 1.0, 1.0, 1.0]

var coefficients = newSeq[tuple[a, b, c: float]]()

for i in 0..3:

coefficients.add((a[i], b[i], c[i]))

for (x, y, z) in coefficients:

echo &"The roots for {x:.2f}x² + {y:.2f}x + {z:.2f}"

echo &"\tx₀ = ", quadRoots(x, y, z)</lang>

{{out}}

<pre>

The roots for 2.00x² + 10.00x + 1.00

x₀ = [(-0.10435607626104, -0.0), (-2.39564392373896, 0.0)]

The roots for 1.00x² + 2.00x + 1.00

x₀ = [(-0.5, 0.0), (0.0, 0.0)]

The roots for 1.00x² + -1000000000.00x + 1.00

x₀ = [(1000000000.0, 0.0), (1e-09, 0.0)]

The roots for 10.00x² + 1.00x + 1.00

x₀ = [(-0.005000000000000001, 0.09987492177719091), (-0.005, -0.0998749217771909)]

</pre>