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# Polynomial Arithmetic

From profit/cost models to the flight of a baseball to approximating the motion of a wave, polynomials are a mathematical way to represent values which are sums of powers of variables.

How many real values of \(x\) satisfy the following equation \(9^x - 6 \cdot 3^x - 55 = 0\)?

Given that \[ax^2+bx+c+7x^2+8x-12=0\] is an algebraic identity, what is the value of \(abc\)?

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