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Omni-MATH / Let S be the set of points (a,b) with 0≤a,b≤1 such that the equation x⁴+ax³−bx²+ax+1=0 has at least one real root. Determine the area of the graph of S.

Problem

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problem

Let SS be the set of points (a,b)(a, b) with 0≤a,b≤10 \leq a, b \leq 1 such that the equation x4+ax3−bx2+ax+1=0x^{4}+a x^{3}-b x^{2}+a x+1=0 has at least one real root. Determine the area of the graph of SS.
Plain-text mathematical notation (without MathML)
Let S be the set of points (a,b) with 0≤a,b≤1 such that the equation x⁴+ax³−bx²+ax+1=0 has at least one real root. Determine the area of the graph of S.
Original LaTeX notation
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 $S$.

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Source and history

task_id
7ce00e18-12c3-5393-9b1a-6b1595bea7cc
task_key
test--7ce00e18-12c3-5393-9b1a-6b1595bea7cc
task_revision_id
1
config / split
/ test

Official source

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