Teaching Kids Programming: Videos on Data Structures and Algorithms
Given a quadratic equation 
it has two real roots (which could be the same) if and only if 
Proof of Quadratic Equation Roots
Let’s move c to the other side: 
And multiply both sides with 4a so we get 
And add term 
and this becomes 
Transform left side: 
Thus, we have two roots:
As these two roots are symmetric so we can get the symmetric axis for a quadratic equation is 
Python Function to Compute Real Roots of a Quadratic Equation
We need to check the case when a is zero or the function does not intersect the X-axis (no real roots).
1 2 3 4 5 6 7 8 9 | def realRootsForQuadraticEquation(a, b, c): if a == 0: raise ValueError("a can't be zero") if b*b-4*a*c < 0: raise Exception("No real roots for {}x^2+{}x+{}=0".format(a, b, c)) r = sqrt(b*b-4*a*c) x1 = (-b + r) / (2 * a) x2 = (-b - r) / (2 * a) return (x1, x2) |
def realRootsForQuadraticEquation(a, b, c):
if a == 0:
raise ValueError("a can't be zero")
if b*b-4*a*c < 0:
raise Exception("No real roots for {}x^2+{}x+{}=0".format(a, b, c))
r = sqrt(b*b-4*a*c)
x1 = (-b + r) / (2 * a)
x2 = (-b - r) / (2 * a)
return (x1, x2)We are returning the roots as a tuple. The time and space complexity is O(1).
–EOF (The Ultimate Computing & Technology Blog) —
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