A more accurate quadratic solution
These examples show the effects of rounding errors in the simple quadratic equation sloving spreadsheet from 13A and a slighty improved version that is more accurate.
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Download spreadsheet with errors (.xlsx) Download improved spreadsheet (.xlsx) Download Python code with error Download improved Python codeSimple quadratic solution with rounding errors – spreadsheet
Improved quadratic solution with rounding errors – spreadsheet
Simple quadratic equation solution with rounding errors – Python
import math
# Enter the coefficients of the
# quadratic equation ax^2+bx+c
# below
a = 1/10000
b = -999999999/100000000
c = -1/1000
# Simple solution
d = b*b-4*a*c
print ( "Discriminant = ",d)
if d < 0:
print ("No real solution")
exit()
x1 = (-b-math.sqrt(d))/(2*a)
x2 = (-b+math.sqrt(d))/(2*a)
print("x = ",x1," or ",x2)
# Output:
#
# Discriminant = 100.00000019999999
# x = -9.99999993922529e-05 or 100000.0
Improved quadratic equation solution – Python
import math
# Enter the coefficients of the
# quadratic equation ax^2+bx+c
# below
a = 1/10000
b = -999999999/100000000
c = -1/1000
# Solution that reduces rounding errors
d = b*b-4*a*c
print ( "Discriminant = ",d)
if d < 0:
print ("No real solution")
exit()
if b < 0:
q = -0.5 * (b-math.sqrt(d))
else:
q = -0.5 * (b+math.sqrt(d))
x1 = q/a
x2 = c/q
print("x = ",x1," or ",x2)
# Output:
#
# Discriminant = 100.00000019999999
# x = 100000.0 or -0.0001
The easiest way to experiment with the Python code is to click on Copy code above and then paste it into any online interpreter – such as this one from Python Principles.
The simple spreadsheets and python examples on this page may be copied freely.