Question 1129264: Find an nth-degree polynomial function with real coefficients satisfying the given conditions.
N=3
-4 and 8+2 are zeros
F(2)=240 Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find an nth-degree polynomial function with real coefficients satisfying the given conditions.
N=3
-4 and 8+2i are zeros
F(2)=240
------
8-2i must also be a zero
-------
F(x) = a(x+4)(x-8-2i)(x-8+2i)
-------
F(x) = a(x+4)[(x-8)^2-(2i)^2]
F(x) = a(x+4)[x^2-16x+64+4]
F(x) = a(x+4)[x^2-16x+68]
-----
Solve for "a" using F(2) = 240
240 = a(2+4)(4-64+68)
240 = a*6*8
a = 240/48
a = 5
-------------
Ans:: F(x) = 5(x+4)(x^2-16x+68)
------------
Cheers,
Stan H.
----------
(