Question 10
Find all zeros of $f(x)=x^{3}+4 x^{2}+3 x-2$. Enter the zeros separated by commas. Enter exact value, not decimal approximations.
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Answer
Final Answer: The zeros of the function \(f(x)=x^{3}+4 x^{2}+3 x-2\) are \(\boxed{-2, -1 + \sqrt{2}, -\sqrt{2} - 1}\).
Step 1 ：The question is asking to find the zeros of the cubic function \(f(x)=x^{3}+4 x^{2}+3 x-2\). The zeros of a function are the x-values for which the function equals zero.
Step 2 ：To find the zeros of this function, we need to solve the equation \(f(x)=0\), which in this case is \(x^{3}+4 x^{2}+3 x-2=0\).
Step 3 ：The zeros of the function are -2, -1 + \(\sqrt{2}\), and -\(\sqrt{2}\) - 1. These are the x-values for which the function equals zero.
Step 4 ：Final Answer: The zeros of the function \(f(x)=x^{3}+4 x^{2}+3 x-2\) are \(\boxed{-2, -1 + \sqrt{2}, -\sqrt{2} - 1}\).
