Question

Hello! I need some help with this homework question, please? I submitted an answer, but it came back incorrect. Q7

Answer 1

The roots are given below as

`\begin{gathered} x=-4-2i \\ x=-4+2i \\ x=1 \\ x=1 \end{gathered}`

By expanding the roots, we will have

`\begin{gathered} (x+4-2i)(x+4+2i)(x-1)(x-1) \\ (x^2+4x+2xi+4x+16+8i-2xi-8i-4i^2)(x^2-x-x+1) \\ (x^2+4x+4x+20)(x^2-2x+1) \end{gathered}`

By further expansion, we will have

`\begin{gathered} (x^2+4x+4x+20)(x^2-2x+1) \\ (x^2+8x+20)(x^2-2x+1) \\ x^4-2x^3+x^2+8x^3-16x^2+8x+20x^2-40x+20 \\ x^4-2x^3+8x^3+x^2-16x^2+20x^2+8x-40x+20 \\ x^4+6x^3+5x^2-32x+20 \end{gathered}`

Hence,

The equation of the polynomial is

`x^4+6x^3+5x^2-32x+20`