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Form a polynomial f(x) when the degree is 5 and the zeros are 2, -i, i, 1-i, 1+i

 Sep 27, 2020
 #1
avatar+27778 
+2

(x-2)(x+i)(x-i)(x -1+i)(x-1-i) =   polynomial 

    multiply all of this out to get:

 

x5 - 4x4 + 7x3 - 8x2 +6x -4

 Sep 28, 2020
 #2
avatar+10336 
+2

Form a polynomial f(x) when the degree is 5 and the zeros are 2, -i, i, 1-i, 1+i

 

Hello Guest!

 

\(\color{blue}f(x)=(x+i)(x-i)(x-1+i)(x-1-i)(x-2)\\ =(x^2+1)(x-2)(x^2-x-ix-x+1+i+ix-i+1)\\ =(x^2+1)(x-2)(x^2-2x+2)\\ =(x^2+1)(x^3-2x^2+2x-2x^2+4x-4)\\ =(x^2+1)(x^3-4x^2+6x-4)\)

\(=x^5-4x^4+6x^3-4x^2+x^3-4x^2+6x-4\\ \color{blue}=x^5-4x^4+7x^3-8x^2+6x-4\)

laugh  !

 Sep 28, 2020

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