quadratic_formula_solution_approx.sf

#!/usr/bin/ruby

# Approximation to the solution for x in:
#  a*x^2 + b*x + c = 0

# Defined only in the following cases:
#  a > 0
#  c < 0

func quadratic_formula_approx(x, y, z, r=300) {

    # say abs(((-y + sqrt(y*y - 4*x*z))/ (2*x)))

    var A = x.abs
    var B = y.abs
    var C = z.abs

    var B1 = (y > 0 ? -y : 0)
    var C1 = (z > 0 ? -z : 0)

    func a(n) is cached {

        return 0 if (n == 0)
        return 1 if (n == 1)

        (B*a(n-1) + A*a(n-2) + B1)/C + C1
    }

    func b(n) is cached {

        return 1 if (n == 0)
        return 0 if (n == 1)

        (B*b(n-1) + A*b(n-2) + B1)/C + C1
    }

    a(r) / b(r)
}

say quadratic_formula_approx(13, -42, -34)       #=> 3.90117814740055779908605856794532743125765386019
say quadratic_formula_approx(1, -1, -1)          #=> 1.61803398874989484820458683436563811772030917981
say quadratic_formula_approx(29, 5, -4)          #=> 0.295057661853378981552427771067600924446979990392