Palindromes in math!

Algebra Level 5

\[\large\displaystyle{{ x }^{ 4 }+{ a }x^{ 3 }+b{ x }^{ 2 }+ax+1=0}\]

If the quartic equation has at least one real root for real numbers \(a\) and \(b\), then find minimum value of \(a^2 + b^2 \).

Source: Asked in my test.
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