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Write a polynomial function  f​ of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form.

3, 4+i​

 Mar 11, 2021
 #1
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If 4 + i  is a root, so is  4-i

 

The polynomial will be of  degree 3  and will be  of  the form   ax^3 +bx^2  + cx + d

 

a  =   1

b  = the  sum of the roots  = - ( 3 + 4+i + 4 - i)  =  -11

c =  (3(4+i)  + 3(4 -i)  + (4 + i) (4 - i) )   =  ( 12 + 3i + 12 - 3i  + 16 - i^2)  =  (40 - - 1)   = 41

d =  -  [ (3) (4 + i) ( 4- i) ] =  - [ 3 ( 16 - i^2)]  = - [3 * 17]   =  -51

 

So....the polynomial  is

 

x^3  - 11x^2  +  41x   -  51

 

 

cool cool cool

 Mar 11, 2021

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