Question

find all of the zeros of p (x) = x^3-x^2+2, given that 1-i is a zero. (if there is more than one zero, separate them with commas.)

Answer 1

We have the next polynomial function

$P(x)=x^3-x^2+2$

In order to find the zero we punt the function equal to zero

$x^3-x^2+2=0$

We have a given zero that is 1-i

x=1-i

than means that we need the conjugate of the zero given is also a zero

x=1+i

and then we need a third zero because the polynomial has third-degree it can be calculated if we factorize the polynomial given

$\mleft(x-1-i\mright)\mleft(x-1+i\mright)\mleft(x+1\mright)=0$

Therefore the zeros are

x=-1

x=1-i

x=1+i