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Using a graphing calculator, find the real zeros of the function:

\[ f(x) = x^8 + 8x^7 - 28x^6 - 60x^5 + 70x^4 - 60x^3 + 28x^2 + 8x + 1. \]

The real zeros are ___

Answer :

Final answer:

To find the real zeros of the function given, one would use a graphing calculator to plot the function and identify where it crosses the x-axis, indicating the real zeros. While specifics cannot be given without actually seeing the graph, the process involves using the calculator's graphing and zero-finding features.

Explanation:

The question asks about finding the real zeros of the function f(x) = x⁸ + 8x⁷ - 28x⁶ - 60x⁵ + 70x⁴ - 60x³ + 28x² + 8x + 1 using a graphing calculator. To do this, you would enter the function into your graphing calculator and use the graphing feature to plot the function. By examining where the graph crosses the x-axis, you can identify the points at which f(x) = 0, which are the real zeros of the function. Since this is an eighth-degree polynomial, there could be up to eight real zeros, but without a specific graphing calculator response here, we can't provide the exact zeros. Generally, finding these zeros involves looking at the graph for x-intercepts and possibly using the calculator's zero or root-finding feature to get precise values. Remember, real zeros are the x-values where the function crosses or touches the x-axis.

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