2022 AMC 12A Problems/Problem 15: Difference between revisions
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==Problem== | ==Problem== | ||
The roots of the polynomial | The roots of the polynomial <math>10x^3 - 39x^2 + 29x - 6</math> 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 | ||
<math>10x^3 - 39x^2 + 29x - 6</math> | |||
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? | units. What is the volume of the new box? | ||
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- phuang1024 | - phuang1024 | ||
==See also== | |||
{{AMC12 box|year=2022|ab=A|num-b=14|num-a=16}} | |||
{{MAA Notice}} | |||
Revision as of 19:47, 11 November 2022
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 
- phuang1024
See also
| 2022 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 14 |
Followed by Problem 16 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
These problems are copyrighted © by the Mathematical Association of America. 
