Answer:[tex]P(x)=x^3-10x^2+13x+74[/tex]
Step-by-step explanation: We are given roots of a third degree polynomial function -2, 6+i.
Note: a radical always comes with pair of plus and minus sign.
Therefore, there would be one more root 6-i.
So, all the roots would be -2, 6+i, 6-i.
So, the factors of polynomial function would be
(x+2)(x-6-i)(x-6+i)
Multiplying those factors,
[tex](x+2)(x^2-6x+xi -6x+36-6i-ix+6i-i^2)[/tex]
[tex](x+2)(x^2-12x+36+1)[/tex]
[tex](x+2)(x^2-12x+37)[/tex]
[tex]x^3-12x^2+2x^2+37x-24x+74[/tex]
[tex]=x^3-10x^2+13x+74[/tex]
Therefore,
[tex]P(x)=x^3-10x^2+13x+74[/tex]
