Final answer:
To approximate the real zero of the function f(x) = x³ + x + 1 to the nearest tenth, we can use the Newton-Raphson method. By applying the Newton-Raphson method, we find that the approximate real zero to the nearest tenth is x = -1.3.
Step-by-step explanation:
To approximate the real zero of the function f(x) = x³ + x + 1 to the nearest tenth, we can use the Newton-Raphson method. The Newton-Raphson method is an iterative process that helps us find the zeros of a function.
1. Start with an initial estimate for the zero. Let's take x = 0 as our initial estimate.
2. Use the formula xn+1 = xn - f(xn) / f'(xn) to update the estimate.
3. Repeat step 2 until the estimate converges to the desired accuracy.
By applying the Newton-Raphson method to f(x) = x³ + x + 1, we find that the approximate real zero to the nearest tenth is x = -1.3.