Uitwerking: ABC-formule
from math import sqrt
a = 3
b = 3
c = -5
D = b*b - 4*a*c
x0 = (-b - sqrt(D)) / (2*a)
x1 = (-b + sqrt(D)) / (2*a)
print(x0, x1)
# Uitgebreide uitwerking
def abc(a, b, c):
D = b**2 - 4*a*c
x0 = (-b - sqrt(D)) / (2*a)
x1 = (-b + sqrt(D)) / (2*a)
return (x0, x1)
print(abc(3, 3, -5))
# uitwerking met relevante polynomen
a,b,c = 1, 7, -18
D = b**2 - 4*a*c
x0 = (-b - sqrt(D)) / (2*a)
x1 = (-b + sqrt(D)) / (2*a)
print(x0, x1)
a,b,c = 1, 6.28318, -9.86959
D = b**2 - 4*a*c
x0 = (-b - sqrt(D)) / (2*a)
x1 = (-b + sqrt(D)) / (2*a)
print(x0, x1)
a,b,c = 3, -12, 0
D = b**2 - 4*a*c
x0 = (-b - sqrt(D)) / (2*a)
x1 = (-b + sqrt(D)) / (2*a)
print(x0, x1)
a,b,c = 2, -37, 1
D = b**2 - 4*a*c
x0 = (-b - sqrt(D)) / (2*a)
x1 = (-b + sqrt(D)) / (2*a)
print(x0, x1)
# Uitgebreide uitwerking
def quadform(a, b, c):
return [(-b + s * sqrt(b**2 - 4*a*c)) / (2*a) for s in (-1, 1)]
trials = [(1, 7, -18),
(1, 6.28318, -9.86959),
(3, -12, 0),
(2, -37, 1)
]
for trial in trials:
print(quadform(*trial))
# de vergelijking x**2 + 5*x + 7 = 0 gaat natuurlijk fout, want:
a, b, c = 1, 5, 7
D = b**2 - 4*a*c
print('D < 0:', D < 0)
