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Form a third degree polynomial function with real coefficients such that 7+i and 6 are zeros

 Apr 3, 2020
 #2
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If  7 + i  is  a zero, then so  is  7  - i

 

So  we  have

 

( x - (7 + i) )  ( x  - (7 + i))  ( x -6)

 

[ x^2  - (7 - i)x  - (7 + i)x  +  ( 7 + i) ( 7 - i)] ( x - 6)

 

[ x^2 -7x + ix  - 7x -ix + 49 - i^2 ] ( x - 6)

 

[ x^2  - 14x + 49 - (-1)  ]   ( x - 6)

 

(x^2  - 14x  +  50)  ( x - 6)

 

x^3 - 14x^2 + 50x

      -6x^2   + 84x  - 300

____________________

x^3 - 20x^2 + 134x  - 300

 

 

 

cool cool cool

 Apr 3, 2020

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