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The length of the segment between the points $(2a, a-4)$ and $(4, -1)$ is $2\sqrt{10}$ units. What is the product of all possible values for $a$?

 
 Apr 7, 2021
 #1
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$(2a-4)^2+(a-3)^2=40$

$4a^2-16a+16+a^2-6a+9=40$
$5a^2-22a+25=40$

$5a^2-22a-15=0$.

 

The product is $-\frac{15}{5}=\boxed{-3}$ by Vieta.

 
 Apr 7, 2021

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