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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 2, 2019
 #1
avatar+18305 
+1

Distance between the two points is given by the distance formula

(2a-4)^2  +  ((a-4)--1)^2

4a^2 -16a+16    +  a^2-6a +9  = (2 sqrt10)^2

5 a^2 -22a + 25 = 40

5a^2-22a - 15 = 0

a = 5 or -3/5        (by Quadratic Formula)

 

5 * -3/5 =    -3

 Apr 2, 2019
 #2
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what do you mean by Quadratic Formula

 Apr 2, 2019
 #3
avatar+4259 
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\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\), so you can find the values !

 Apr 2, 2019
 #4
avatar+18305 
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Agree with Tertre....

5a^2-22a - 15 = 0

Use Quadratic Formula   (as Tertre posted)   a = 5   b = -22   c = -15     to find the possible values of 'a' in the equation

ElectricPavlov  Apr 2, 2019

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