input: import math
  
  def poly(coefficients: list, x: float):
      """
      Compute the value of a polynomial defined by coefficients at a specific x.
      Returns the sum: coefficients[0] + coefficients[1] * x + coefficients[2] * x^2 + ... + coefficients[n] * x^n
      """
      return sum([c * math.pow(x, index) for index, c in enumerate(coefficients)])
  
  def find_zero(coefficients: list):
      """ Given a list of polynomial coefficients, determine a zero of the polynomial.
      The function find_zero returns a root x such that the polynomial evaluates to zero.
      It is designed to accept only lists with an even number of coefficients and where the highest non-zero coefficient guarantees a solution.
      >>> round(find_zero([1, 2]), 2) # Polynomial is f(x) = 1 + 2x
      -0.5
      >>> round(find_zero([-6, 11, -6, 1]), 2) # Derived from (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
      1.0
      """
output:     import math
  
  def find_zero(coefficients: list):
      def poly(coefficients: list, x: float):
          return sum([c * math.pow(x, index) for index, c in enumerate(coefficients)])
  
      def derivative(coefficients: list):
          return [index * c for index, c in enumerate(coefficients)][1:]
  
      def newton_method(coefficients: list, initial_guess: float = 0.0, tolerance: float = 1e-7, max_iterations: int = 1000):
          x = initial_guess
          for _ in range(max_iterations):
              fx = poly(coefficients, x)
              if abs(fx) < tolerance:
                  return x
              f_prime_x = poly(derivative(coefficients), x)
              if f_prime_x == 0:  # Avoid division by zero
                  break
              x -= fx / f_prime_x
          raise ValueError("Failed to converge")
  
      return newton_method(coefficients, initial_guess=0.0)