# Vieta: An Opera in Two Acts by Andrei Golovanov

Algebra Level 4

A picture of the scene The lights turn on, the curtain opens and Act One of the world-famous opera, Vieta, commences.

"The sum of the roots of $$4x^{12}-36x^{11}+3x^7+7x^2+1=0$$ is $$A$$. Let me introduce performer Gustav von $$A$$!"

Loud round of applause. Gustav von $$A$$ sings The Joy of Vieta, by Wolfram Alphaeus Mozart. The curtain drops.

After a short interlude, the curtain reopens to reveal a brightly lit stage. In big letters is written $$3Ax^3-3=0$$. Gustav von Schnieber appears to a roar of applause and sings a solo piece in basso: The Product of the Roots of that 'Nomial. He finishes by revealing that number. What was it? (It is a recurring number so just input the first few decimal places. Gustav von Schnieber, however, is still on stage finishing saying it!)

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