如何求方程f(x)=0的所有可能形式x=p(x)

def solve_equation(f, p, x0, epsilon=1e-6, max_iter=100):
    x = x0
    for i in range(max_iter):
        x_new = p(x)
        if abs(x_new - x) < epsilon:
            return x_new
        x = x_new
    return None

# 示例方程 f(x) = x^2 - 2
def f(x):
    return x**2 - 2

# 示例迭代函数 p(x) = x - f(x)/f'(x)
def p(x):
    return x - f(x) / (2 * x)

# 调用示例
root = solve_equation(f, p, 1.5)
if root is not None:
    print("方程的根为:", root)
else:
    print("未找到方程的根")