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 ?

Question

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 ?

anonymous · Answer

(2a - 4)^2 + (a - 4 -(-1))^2 

= (2a - 4)^2 + (a - 3)^2 

= (4a^2 -16a + 16 + a^2 - 6a + 9

= 5a^2 - 22a + 25

sqrt(5a^2 - 22a + 25) = 2 sqrt(10)

pm (5a^2 - 22a +25) = 40

anonymous · Answer

5a^2 - 22a - 15 = 0


and

-5a^2 + 22a - 65 = 0

anonymous · Answer

40*0=0 the answer is 0?

anonymous · Answer

nope not!

anonymous · Answer

using distance formula,
(2a-4)^2 + (a-4+1)^2 = sq(2sqrt(10))
4a^2 -16a +16 +a^2 -6a +9 = 40
5a^2 -22a + 25 = 40
5a^2 - 22a -15 =0
5a^2 - 25a + 3a -15 =0
5a(a-5) + 3(a-5) = 0
(5a + 3) ( a-5) = 0
a = -3/5  or 5
 so 
product = -3

anonymous · Answer

i was late coz i  did some mistake in addition previously if you have noticed that

anonymous · Answer

are u still confused with this solution