# MCS 260 Fall 2021 Lecture 4
# Determine the number of real roots of
# a quadratic polynomial
# We read a polynomial
# ax**2 + bx + c
# by asking for a, b, c separately
print("Enter the coefficients a, b, c")
print("of a quadratic polynomial ax**2 + bx + c")
print("one per line.")
a = float(input())
b = float(input())
c = float(input())
print("Concerning the quadratic polynomial")
print(a,"x**2 +",b,"x +",c)
# discriminant of ax**2+bx+c is b**2 - 4ac
# discriminant is zero exactly when the poly
# is a perfect square
disc = b*b - 4*a*c
# disc < 0 means no real roots
# disc == 0 means one real root
# disc > 0 means two real roots
# TODO: Handle the case where a is zero
# reporting that it isn't actually a quadratic!
if disc < 0.0:
print("This polynomial has no real roots.")
elif disc == 0.0:
print("This polynomial has exactly one real root.")
print("(It's a perfect square.)")
else:
print("This polynomial has two real roots.")