Question

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.-1,3-i

Answer 1

`(x+1)\cdot(x-(3-i))\cdot(x-(3+i))=0`
`\begin{gathered} (x+1)\cdot(x-3+i)(x-3-i)=0 \\ (x+1)\cdot(x^2-3x-ix-3x+9+3i+ix-3i-i^2)=0 \\ (x+1)\cdot(x^2-6x+9-(-1))=0 \\ (x+1)\cdot(x^2-6x+10)=0 \\ x^3-6x^2+10x+x^2-6x+10=0 \\ x^3-5x^2+4x+10=0 \end{gathered}`

So the polynomial f(x) of degree 3 is

`f(x)=x^3-5x^2+4x+10`