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  1. def sqrt(n):
  2.     x = n
  3.     y = 1.0
  4.     eps = 0.00001
  5.     while x - y > eps:
  6.         x = (x + y) / 2
  7.         y = n / x
  8.     return x
  9. # Viete's rules = Relatiile lui Viete
  10. # ax^2 + bx + c = 0; a != 0
  11. # x^2 - Sx + P = 0
  12. # S = x1 + x2
  13. # P = x1 * x2
  14. # S = -b/a; P = c/a
  15. # the study of the sign roots of a Quadratic Equation
  16. def Nature_Roots_Quadratic_Equation(a, b, c):
  17.     d = b ** 2 - 4 * a * c
  18.     #a!=0
  19.     S = -b/a
  20.     P = c/a
  21.  
  22.     print(f"Sum = {S}, Prod = {P}")
  23.     print("Sum = %.2f Prod = %.2f"%(S, P))
  24.     if d < 0:
  25.         return ["imaginary"]
  26.     elif d >= 0:
  27.          x1 = ( -b - sqrt(d) )/ (2*a)
  28.          x2 = ( -b + sqrt(d) ) / (2*a)
  29.          print(f"x1={x1:.2f} x2={x2:.2f}")
  30.          if S > 0:
  31.              if P > 0:
  32.                  return ["x1>0","x2>0"]
  33.              elif P < 0:
  34.                  return ["x1<0","x2>0","|x1|<|x2|"]
  35.                  #x1=-3, x2=7
  36.              else:
  37.                  return ["x1=0","x2>0"]
  38.          # S < 0
  39.          else:
  40.              if P > 0:
  41.                  return ["x1<0","x2<0"]
  42.              elif P < 0:
  43.                  return ["x1<0","x2>0","|x1|>|x2|"]
  44.              else:
  45.                  return ["x1=0","x2<0"]
  46. def main():
  47.  
  48.     lesson = dict(title = "Viete's Rules", content ="\nNature Roots Quadratic Equation")
  49.  
  50.     print("Today we'll learn about:\n{title} {content}".format(**lesson))
  51.  
  52.     A = 1
  53.     B = 5
  54.     C = 2
  55.     print(*Nature_Roots_Quadratic_Equation(A,B,C), sep="\n")
  56.  
  57. main()
  58.  
Success #stdin #stdout 0.04s 9788KB
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Today we'll learn about:
Viete's Rules 
Nature Roots Quadratic Equation
Sum = -5.0, Prod = 2.0
Sum = -5.00 Prod = 2.00
x1=-4.56 x2=-0.44
x1<0
x2<0
https://ideone.com/ekm6kL
Nature Roots Quadratic Equation based on Viete's formulas
language:
Python 3 (python  3.9.5)
created:
188 days ago
visibility:
secret

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