2022 AMC 12A Problems/Problem 15
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Problem
The roots of the polynomial
are the height, length, and width of a rectangular box (right rectangular prism. A new rectangular box is formed by lengthening each edge of the original box by 2 units. What is the volume of the new box?
Solution
Let ,
,
be the three roots of the polynomial. The lenghtened prism's area is
.
By vieta's formulas, we know that:
.
We can substitute these into the expression, obtaining
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