Answer:
[tex]x^3-x^2(4+i\sqrt{3} )+x(5+i2\sqrt{3} )-(2+i\sqrt{3} )=0[/tex]
Step-by-step explanation:
We have given that this polynomial has the given zeroes of 1, 1, and [tex]2+i\sqrt{3}[/tex], we can express the polynomial in a factored form where each zero has the form x-a (where a is our zero):
polynomial= [tex](x-1) (x-1) (2+i\sqrt{3})[/tex]
=[tex](x^2+1-2x) (2+i\sqrt{3})[/tex]
=[tex]x^3-x^2(4+i\sqrt{3} )+x(5+i2\sqrt{3} )-(2+i\sqrt{3} )=0[/tex]
