SOLUTION: the area of a rectangle is x^2-11x+24 what are the dimensions

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Question 866887: the area of a rectangle is x^2-11x+24 what are the dimensions
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The polynomial must be positive VALUE and x must be a positive VALUE. The polynomial is not factorable. As a function, the polynomial opens upward and has a minimum.

roots:
x=%2811%2B-+sqrt%28121-4%2A24%29%29%2F2
x=%2811%2B-+sqrt%28121-96%29%29%2F2
x=%2811%2B-+sqrt%2825%29%29%2F2
The PLUS sqrt is necessary.
x=%2811%2B5%29%2F2
x=8

highlight%28x%3E8%29 necessary
So either dimension MUST highlight%28DIMENSION%3E%28x-8%29%29 for domain highlight%28x%3E8%29.


A graph of the fun0ction may help.
graph%28300%2C300%2C-1%2C12%2C-2%2C14%2Cx%5E2-11x%2B24%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+x%5E2-11x%2B24=0... factor completely and find the roots; write -11x as -8x-3x
x%5E2-8x-3x%2B24=0......group
%28x%5E2-8x%29-%283x-24%29=0 ......factor
x%28x-8%29-3%28x-8%29=0
%28x-3%29%28x-8%29=0
solutions
if x-3=0=> x=3
if x-8=0=> x=8
so, the dimensions of a rectangle are: the length is 8 and the width is 3