Teaching Kids Programming – Finding Real Roots of a Quadratic Equation

ACMer

4 years ago

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).

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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Proof of Quadratic Equation Roots

Python Function to Compute Real Roots of a Quadratic Equation

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