from math import sqrt
a=1e-8
b=10
c=1e-8
x1 = ((-b)-sqrt((b**2)-(4*a*c)))/(2*a)
x2 = ((-b)+sqrt((b**2)-(4*a*c)))/(2*a)
print 'x1 = {}'.format(x1)
print 'x2 = {}'.format(x2)
print (4*a*c)
print (sqrt(b**2-4*a*c))
print b**2
print 2*a
When I run the program, this returns:
x1 = -1e+09
x2 = 0.0
4e-16
10.0
100.0
2e-08
What I need is for x2 to be equal to -1e-9.
The problem seems to be with the
sqrt((b**2)-(4*a*c))
as it gives 10 as a result, obviously because 4*(10^-8)*(10^-8) is almost equal to 0, and is considered 0 by python.
This results in:
sqrt((b**2)-(4*a*c)) = sqrt(b**2) = sqrt(10**2) = 10
Any help would be greatly appreciated
Use the decimal module:
from decimal import Decimal
a = Decimal('1E-8')
b = 10
c = Decimal('1E-8')
x1 = ((-b)-((b**2)-(4*a*c)).sqrt())/(2*a)
x2 = ((-b)+((b**2)-(4*a*c)).sqrt())/(2*a)
print 'x1 = {}'.format(x1)
print 'x2 = {}'.format(x2)
results in
x1 = -999999999.999999999000000000
x2 = -1.0000000000E-9