polynomial

(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

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

Hello Guest!

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

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

  !