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devlian [24]
3 years ago
15

Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ uti

lity, use it to graph the function and verify the real zeros and the given function value.
n=3
4 and 4i are zeros;
f(-1)=85

F(x) = ________
Mathematics
1 answer:
Elan Coil [88]3 years ago
3 0

Givem that at n = 3: 4 and 4i are zero;

Then;

(x - 4)(x - 4i)(x + 4i) \: (x - 4)( {x}^{2}  - ( {4i)}^{2}  \\ (x - 4)(x - 4i)(x + 4i) \: (x - 4)( {x}^{2}  + 16) \\ (x - 4)(x - 4i)(x + 4i) \:  {x}^{3}  + 16x -  {4x}^{2}  - 64 \\ (x - 4)(x - 4i)(x + 4i) \:  {x}^{3}  -  {4x}^{2}  + 16x - 64

Hence the function is:

f =  {x}^{3}  - {4x}^{2}  + 16x - 64

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