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Suppose  is a polynomial of degree five for which g(1) = 2, g(2) = 3, g(3) = 4, g(4) = 5, g(5) = 6, and g(6) = -113. Find g(0).
 

 Jan 12, 2019
 #1
avatar+98154 
+2

We have this sytem of 6 equations

 

a + b + c + d + e + f =  2,

32a + 16b + 8c + 4d + 2e + f = 3,

243a + 81b + 27c + 9d + 3e + f = 4,

1024a + 256b + 64c + 16d + 4e + f = 5,

3125a + 625b + 125c + 25d + 5e + f =  6,

7776a + 1296b + 216c + 36d + 6e + f = -113 

 

This system is very tedious to solve by hand  [ so...I won't ]

 

We are only interested in the value of   "f"  because this will be the y intercept for g(0)

 

Using a matrix calculator......f is shown to be 121  = g(0)

 

 

cool cool cool

 Jan 12, 2019
 #3
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0

Thanks

Guest Jan 14, 2019
 #2
avatar+524 
0

lol thats very dumb equations :P

 Jan 12, 2019

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