75 lines
1.6 KiB
Python
75 lines
1.6 KiB
Python
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#!/usr/bin/python3
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from math import sqrt
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from util.io import readvalue
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def solution_count(a, b, c):
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"""
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Calculates the number of real solutions
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for a*x**2 + b*x + c = 0.
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Returns: 0 or 1 or 2
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Method:
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After doing some fiddling you can get the equation
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(x + b/(2*a))**2 = (b/(2*a))**2 - c/a
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You can derive that the equation has
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no real solution, if (b/(2*a))**2 - c/a < 0
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one real solution, if (b/(2*a))**2 - c/a = 0,
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two real solutions, if (b/(2*a))**2 - c/a > 0.
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"""
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rterm = (b/(2*a))**2 - c/a
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if(rterm < 0):
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return 0
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if(rterm == 0):
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return 1
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if(rterm > 0):
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return 2
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def solutions(a, b, c):
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"""
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Returns the solution(s) of a*x**2 + b*x + c = 0.
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If the equation has no solution, it returns None,
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a tuple of the soltions, otherwise.
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"""
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# Get the number of solutions:
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number_of_solutions = solution_count(a, b, c)
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if(not number_of_solutions):
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return
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if(number_of_solutions == 1):
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return (-b / (2*a), )
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else:
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rterm = sqrt((b/(2*a))**2 - c/a)
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return (-b / (2*a) + rterm, -b / (2*a) - rterm)
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if( __name__ == "__main__"):
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print("Program to find the solution(s) for a*x**2 + b*x + c = 0")
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a = readvalue("a > ", float)
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b = readvalue("b > ", float)
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c = readvalue("c > ", float)
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number_of_solutions = solution_count(a, b, c)
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messages = ["There are no real solutions."
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, "There is exactly one real solution."
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, "There are exactly two real solutions."]
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print(messages[number_of_solutions])
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if(number_of_solutions == 1):
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print("The solution is:", solutions(a, b, c)[0])
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if(number_of_solutions == 2):
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print("The first solution is:", solutions(a, b, c)[0])
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print("The second solution is:", solutions(a, b, c)[1])
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