Quadratic equation solver not working

Question

I'm trying to create a quadratic equation solver but it doesn't seem to be working when I put in a coefficient greater than 1? The code and error message is below. Any help is greatly appreciated.

print "Welcome to the quadratic equation solver."
print "The general quadratic equation = ax^2 + bx + c.\n"

def POS(a,b):
#This function gives the point at which the quadratic turns
    tp = float((-b)/(a*2))
    return (tp)

#This allows for the user to input the values of the variables
while True:
    s = raw_input ("Please insert a numerical value for a: ")
    try:
        a = float(s)
        break
    except ValueError:
        print "Please enter a numeric value."
print ("Well done.\n")

while True:
    s = raw_input ("Please insert a numerical value for b: ")
    try:
        b = float(s)
        break
    except ValueError:
        print "Please enter a numeric value."
print ("Well done.\n")

while True:
    s = raw_input ("Please insert a numerical value for c: ")
    try:
        c = float(s)
        break
    except ValueError:
        print "Please enter a numeric value."
print ("Well done.\n")

#This uses the function to give the co-ordinate of the turning point
print POS(a,b), "is the x-value of the turning point"
print ((a)*(POS(a,b)**2))+((b)*POS(a,b))+c, "is they y-value of the turning point. \n"

#This tells whether the quadratic is positive or negative
if a >0:
    print "The quadratic is positive.\n"

if a<0:
    print "The quadratic is negative.\n"

#This determines the root of the quadratic
root1 = (-b +((b**2) - (4*a*c))**0.5) / (2 * a)
root2 = (-b -((b**2) - (4*a*c))**0.5) / (2 * a)
print "The quadratic has a root at x =",root1
if root1 != root2:
    print "The quadratic has another root at x =",

#This uses the discriminant to determine the nature of the quadratic
if (b**2)-(4*a*c) == 0:
    print root1

elif (b**2)-(4*a*c) > 0:
    print root1 and root2

elif (b**2)-(4*a*c) < 0:
    print "The quadratic contains no roots"

for x in range(-1000,1000):
    quadratic = (a*x**2)+(b*x)+c

#Determines the derivitive and second derivitive of the quadratic
print "The derivitive of the quadratic is: ",2*a,"x", "+",b
print "The second derivitive of the quadratic is"

#Create plot
X = arange (-1000,1000,1)
plot(X, quadratic, linewidth=3, label="quadratic")

#Create title and axes label
title ("Graph of the quadratic")
xlabel ("x")
ylabel ("y")

#grid
grid(True)
legend()
show()

Error message:

Traceback (most recent call last):
  File "C:\Users\Peter\Downloads\test.py", line 49, in <module>
    root1 = (-b +((b**2) - (4*a*c))**0.5) / (2 * a)
ValueError: negative number cannot be raised to a fractional power

Answer 1

You can also switch to Python3 so that instead of a ValueError your number will be implicitly cast to a complex number.

(-2)**.2
(0.9293164906031477+0.6751879523998812j)

Answer 2

Part of your code:

#This determines the root of the quadratic
root1 = (-b +((b**2) - (4*a*c))**0.5) / (2 * a)
root2 = (-b -((b**2) - (4*a*c))**0.5) / (2 * a)
print "The quadratic has a root at x =",root1
if root1 != root2:
    print "The quadratic has another root at x =",

#This uses the discriminant to determine the nature of the quadratic
if (b**2)-(4*a*c) == 0:
    print root1

elif (b**2)-(4*a*c) > 0:
    print root1 and root2

elif (b**2)-(4*a*c) < 0:
    print "The quadratic contains no roots"

for x in range(-1000,1000):
    quadratic = (a*x**2)+(b*x)+c

Let's replace (b**2)-(4*a*c) with D:

#This determines the root of the quadratic
D = (b**2)-(4*a*c)

root1 = (-b +(D)**0.5) / (2 * a)
root2 = (-b -(D)**0.5) / (2 * a)

print "The quadratic has a root at x =", root1
if root1 != root2:
    print "The quadratic has another root at x =",

#This uses the discriminant to determine the nature of the quadratic
if D == 0:
    print root1

elif D > 0:
    # old code:
    # print root1 and root2
    # new code:
    print root1, root2

elif D < 0:
    print "The quadratic contains no roots"

for x in range(-1000,1000):
    quadratic = (a*x**2)+(b*x)+c

Problem in these two lines:

root1 = (-b +(D)**0.5) / (2 * a)
root2 = (-b -(D)**0.5) / (2 * a)

If D is less than 0, this lines will raise ValueError you got. As error message said number cannot be raised to a fractional power. So we have to check if D is less than 0 or not.

#This determines the root of the quadratic
D = (b**2)-(4*a*c)

# new code:
if D >= 0:
    root1 = (-b +(D)**0.5) / (2 * a)
    root2 = (-b -(D)**0.5) / (2 * a)

    print "The quadratic has a root at x =", root1
    if root1 != root2:
        print "The quadratic has another root at x =", root2


#This uses the discriminant to determine the nature of the quadratic
# We've already printed root1 and root2
# if D == 0:
#     print root1

# elif D > 0:
#     print root1, root2

# D < 0
else:
    print "The quadratic contains no roots"

for x in range(-1000,1000):
    quadratic = (a*x**2)+(b*x)+c

Answer 3

#This uses the discriminant to determine the nature of the quadratic
if (b**2)-(4*a*c) == 0:
    print root1

elif (b**2)-(4*a*c) > 0:
    print root1 and root2

elif (b**2)-(4*a*c) < 0:
    print "The quadratic contains no roots"

Perform this check before you process the roots and break if it is a complex root.

>>> a=2
>>> b=4
>>> c=1
>>> delta=math.pow(b,2)-4*a*c
>>> math.sqrt(delta) #raises error for -ve integers
3.4641016151377544 
gamma=math.sqrt(delta)
>>>root1=(-b+gamma)/2/a
>>>root2=(-b-gamma)/2/a

Answer 4

I think the problem with your code is caused due to the following part:

#This determines the root of the quadratic
root1 = (-b +((b**2) - (4*a*c))**0.5) / (2 * a)
root2 = (-b -((b**2) - (4*a*c))**0.5) / (2 * a)
print "The quadratic has a root at x =",root1
if root1 != root2:
    print "The quadratic has another root at x =",

#This uses the discriminant to determine the nature of the quadratic
if (b**2)-(4*a*c) == 0:
    print root1

elif (b**2)-(4*a*c) > 0:

    print root1 and root2

elif (b**2)-(4*a*c) < 0:
    print "The quadratic contains no roots"

Any negative number when raised to a fractional power will return a complex number which the computer is not able to calculate.

In (b**2) - (4*a*c))**0.5 there is a possibility that b**2 is less than 4*a*c. In such a case there would occur a ValueError.

To prevent this: you should structure your code in the following manner-

if (b**2)-(4*a*c) == 0:
    print root1

elif (b**2)-(4*a*c) > 0:
    root1 = (-b +((b**2) - (4*a*c))**0.5) / (2 * a)
    root2 = (-b -((b**2) - (4*a*c))**0.5) / (2 * a)
    print "The quadratic has a root at x =",root1
    if root1 != root2:
       print "The quadratic has another root at x =",
    print root1 and root2

elif (b**2)-(4*a*c) < 0:
    print "The quadratic contains no roots"