A Different Way to Solve Quadratic Equations

This method is pretty fascinating and inspiring.

suppose we have an quadratic equation:

X^2 + a*X + b = 0

a, b is known & constant

if we want to solve this equation to get its root, how do we do that?

definitely it has the classical way Quadratic Formula

however it is not the way we really want.

the following is idea,

we rewrite equation by the multiplication of two unknowns

(X + [1]) * (X + [2]) = 0

by comparison;

[1] + [2] = a
[1] * [2] = b

by using a/2, we surely can have,

(a/2 - u) + (a/2 - u) = a

then the problem becomes, finding u to make;

(a/2 - u) * (a/2 + u) = b

upto here, it becomes extremely simple to get,

1/4 * a^2 - u^2 = b

once u is got, we can back calculate,

[1] = a/2 - u
[2] = a/2 + u

inverse these two roots are the answer that we want to get

python codes

def solve_quadratic_equation(a,b):
    """Solve Quadratic Equation
    Parameter (Number):
        a, b is the parameter in quadratic equation
        X^2 + a*X + b = 0
    Return (Tuple):
        If equation has real roots (1D): (x1, x2)
        otherwise (2D):  ((t1,-t2), (t1,t2))
    """
    t = a*a/4 - b
    if t >= 0:
        u = pow(t,1/2)
        x1 = 0 - (a/2 - u)
        x2 = 0 - (a/2 + u)
    else:
        u = pow(-t,1/2)
        x1 = (-a/2, u)
        x2 = (-a/2, -u)
    return (x1, x2)
  