Question

Enter the polynomial function with the least degree and a leading coefficient of 1 that has the given

zeros. Enter your answer in standard form.
1,-1(multiplicity 3), and 3i

Answer 1

`x^(3) +(2-3i)x^(2) -(3+6i)x+9i`

Explanation:

• if a, b, c are the zeros of a polynomial, then the equation of the curve with leading coefficient of 1 or the polynomial function with leading coefficient of 1 f(x) can be written as : (x-a)* (x-b)* (x-c).

• here, the given zeros are : 1, -3 , 3i

• so, the polynomial function f(x) = (x-1)* (x-(-3))* (x-3i).

=(x-1)* (x+3)* (x-3i)

=
`(x^(2) +2x-3)*(x-3i)\\=x^(3)+2x^(2)  -3x-3ix^(2) -6ix+9i.\\=x^(3) +(2-3i)x^(2) -(3+6i)x+9i`

• thus, the polynomial function with the least degree and a leading coefficient of 1 that has the zeros : 1,-1(multiplicity 3), and 3i is

`x^(3) +(2-3i)x^(2) -(3+6i)x+9i`