Answer :

Final answer:

The real zeros of the function f(x) = x^7 + 13x^5 - 48x^3 can be found by factoring and solving a combination of cubic and quadratic equations.

Explanation:

First, it's important to note that there is a typo in the equation you've given, so let's fix that to be f(x) = x^7 + 13x^5 - 48x^3. This is a polynomial function. The first step to solving for the real zeros of this function is factoring. In this case, we can factor out an x^3 term, simplifying the equation to x^3(x^4 + 13x^2 - 48) = 0. This now gives us a cubic and a quadratic term within the parentheses.

Setting x^3=0, we find that one of the real zeros is x=0. To find the remaining zeros, we must solve the quadratic equation x^4 + 13x^2 - 48=0. This can be solved in the usual way for quadratics, where x represents x^2 values.

Finally, take the square roots of the x^2 values to obtain the actual x values. This will enable you to determine all of the real zeros of the function.

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