Find all real values of $a$ for which the polynomial
\[x^4 + ax^3 - x^2 + ax + 1 = 0\]has at least one real root.
Question:
Find all real values of $a$ for which the polynomial
\[x^4 + ax^3 - x^2 + ax + 1 = 0\]has at least one real root.
Answer:
Let's think step by step.

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\left( -\infty, -\frac{1}{2} \right] \cup \left[ \frac{1}{2}, \infty \right)
Find all real values of $a$ for which the polynomial
\[x^4 + ax^3 - x^2 + ax + 1 = 0\]has at least one real root.
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