input: import math
  
  
  def evaluate_polynomial(coeffs: list, value: float):
      """
      Computes the value of a polynomial with given coefficients at a specific x.
      return coeffs[0] + coeffs[1] * value + coeffs[2] * value^2 + .... coeffs[n] * value^n
      """
      return sum([coeff * math.pow(value, i) for i, coeff in enumerate(coeffs)])
  
  
  def find_root(coeffs: list):
      """ coeffs represent the coefficients of a polynomial.
      find_root determines an x such that the polynomial evaluates to zero.
      find_root returns only a single root, even if there are multiple roots.
      Additionally, find_root only processes lists with an even number of coefficients
      and with the largest non-zero coefficient to ensure a solution exists.
      >>> round(find_root([1, 2]), 2) # f(x) = 1 + 2x
      -0.5
      >>> round(find_root([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
      1.0
      """
output:     
      # Define a tolerance for root-finding algorithm
      TOLERANCE = 1e-7
      
      # Use Newton's method to find the root of the polynomial
      def newton_method(coeffs):
          def derivative(coeffs):
              return [i * coeffs[i] for i in range(1, len(coeffs))]
  
          def poly_value(coeffs, x):
              return sum([coeff * math.pow(x, i) for i, coeff in enumerate(coeffs)])
          
          def poly_derivative_value(coeffs, x):
              deriv_coeffs = derivative(coeffs)
              return sum([coeff * math.pow(x, i) for i, coeff in enumerate(deriv_coeffs)])
          
          x = 0  # Initial guess
          for _ in range(1000):  # Max iterations
              f_value = poly_value(coeffs, x)
              if abs(f_value) <= TOLERANCE:
                  break
              f_derivative_value = poly_derivative_value(coeffs, x)
              if f_derivative_value == 0:
                  break
              x = x - f_value / f_derivative_value
          return x
      
      if len(coeffs) % 2 != 0 or coeffs[-1] == 0:
          raise ValueError("List must have an even number of coefficients and the highest degree coefficient should be non-zero.")
      
      return newton_method(coeffs)
  