HMMT 2008 A9

Let $S$ be the set of points $(a, b)$ with $0 \leq a, b \leq 1$ such that the equation

$x^{4}+a x^{3}-b x^{2}+a x+1=0$

has at least one real root. Determine the area of the graph of $S$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1}{4}

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