确定f(X)的最高实根= 2x^3 - 11.7x^2 +17.7x -5 (使用python)

import sympy as sp

def newton_method(f, x0, epsilon=1e-6, max_iterations=100):
    x = sp.Symbol('x')
    f_prime = sp.diff(f, x)
    f_prime_prime = sp.diff(f_prime, x)
    f_prime_func = sp.lambdify(x, f_prime)
    f_prime_prime_func = sp.lambdify(x, f_prime_prime)
    
    x_n = x0
    iterations = 0
    
    while abs(f_prime_func(x_n)) > epsilon and iterations < max_iterations:
        x_n = x_n - f_prime_func(x_n) / f_prime_prime_func(x_n)
        iterations += 1
    
    return x_n

f = 2 * x**3 - 11.7 * x**2 + 17.7 * x - 5
x0 = 0  # 初始值
root = newton_method(f, x0)
print("最高实根为:", root)

def bisection_method(f, a, b, epsilon=1e-6, max_iterations=100):
    x = sp.Symbol('x')
    f_func = sp.lambdify(x, f)
    
    if f_func(a) * f_func(b) >= 0:
        raise ValueError("函数在给定区间内没有根或有多个根")
    
    x_n = (a + b) / 2
    iterations = 0
    
    while abs(f_func(x_n)) > epsilon and iterations < max_iterations:
        if f_func(a) * f_func(x_n) < 0:
            b = x_n
        else:
            a = x_n
        x_n = (a + b) / 2
        iterations += 1
    
    return x_n

f = 2 * x**3 - 11.7 * x**2 + 17.7 * x - 5
a = 0  # 区间左端点
b = 1  # 区间右端点
root = bisection_method(f, a, b)
print("最高实根为:", root)