From 559bd5dc6f18d36fd25226b22fbbdcc9a0efc32d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20Kn=C3=BCttel?= Date: Wed, 31 Oct 2018 13:48:36 +0100 Subject: [PATCH] Added exercise 7 --- ex_07.py | 74 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 74 insertions(+) create mode 100644 ex_07.py diff --git a/ex_07.py b/ex_07.py new file mode 100644 index 0000000..e3b3d43 --- /dev/null +++ b/ex_07.py @@ -0,0 +1,74 @@ +#!/usr/bin/python3 + +from math import sqrt + +from util.io import readvalue + +def solution_count(a, b, c): + """ + Calculates the number of real solutions + for a*x**2 + b*x + c = 0. + + Returns: 0 or 1 or 2 + + Method: + + After doing some fiddling you can get the equation + + (x + b/(2*a))**2 = (b/(2*a))**2 - c/a + + You can derive that the equation has + no real solution, if (b/(2*a))**2 - c/a < 0 + one real solution, if (b/(2*a))**2 - c/a = 0, + two real solutions, if (b/(2*a))**2 - c/a > 0. + """ + + rterm = (b/(2*a))**2 - c/a + + if(rterm < 0): + return 0 + if(rterm == 0): + return 1 + if(rterm > 0): + return 2 + +def solutions(a, b, c): + """ + Returns the solution(s) of a*x**2 + b*x + c = 0. + + If the equation has no solution, it returns None, + a tuple of the soltions, otherwise. + """ + # Get the number of solutions: + number_of_solutions = solution_count(a, b, c) + + if(not number_of_solutions): + return + + + if(number_of_solutions == 1): + return (-b / (2*a), ) + else: + rterm = sqrt((b/(2*a))**2 - c/a) + return (-b / (2*a) + rterm, -b / (2*a) - rterm) + + + +if( __name__ == "__main__"): + print("Program to find the solution(s) for a*x**2 + b*x + c = 0") + a = readvalue("a > ", float) + b = readvalue("b > ", float) + c = readvalue("c > ", float) + + number_of_solutions = solution_count(a, b, c) + + messages = ["There are no real solutions." + , "There is exactly one real solution." + , "There are exactly two real solutions."] + print(messages[number_of_solutions]) + + if(number_of_solutions == 1): + print("The solution is:", solutions(a, b, c)[0]) + if(number_of_solutions == 2): + print("The first solution is:", solutions(a, b, c)[0]) + print("The second solution is:", solutions(a, b, c)[1])