Question 5
Find all zeros of $f (x) = x^{3} + x^{2} - 8 x - 6$ . Enter the zeros separat decimal approximations.
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The complex zeros of the polynomial function $f (x) = x^{3} + x^{2} - 8 x - 6$ are $- 3$ , $1 - \sqrt{2}$ , and $1 + \sqrt{2}$ .

Steps

Step 1 ：Set the function $f (x) = x^{3} + x^{2} - 8 x - 6$ equal to zero and solve for x to find the real zeros of the polynomial function.

Step 2 ：The real zeros of the polynomial are $- 3$ , $1 - \sqrt{2}$ , and $1 + \sqrt{2}$ .

Step 3 ：Since these zeros are already complex, there is no need to perform synthetic division and solve a quadratic equation.

Step 4 ：Therefore, the complex zeros of the polynomial are $- 3$ , $1 - \sqrt{2}$ , and $1 + \sqrt{2}$ .

Step 5 ：The complex zeros of the polynomial function $f (x) = x^{3} + x^{2} - 8 x - 6$ are $- 3$ , $1 - \sqrt{2}$ , and $1 + \sqrt{2}$ .