Difference between revisions of "2022 AMC 12A Problems/Problem 15"
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<math>a+b+c = \frac{-B}{A} = \frac{39}{10}</math>. | <math>a+b+c = \frac{-B}{A} = \frac{39}{10}</math>. | ||
| − | We can substitute these into the expression, obtaining <math>V = \frac{6}{10} + 2(\frac{29}{10}) + 4(\frac{39}{10}) + 8 = (D) 30</math> | + | We can substitute these into the expression, obtaining <math>V = \frac{6}{10} + 2(\frac{29}{10}) + 4(\frac{39}{10}) + 8 = \boxed{(D) 30}</math> |
- phuang1024 | - phuang1024 | ||
Revision as of 20:51, 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
