Question

(Algebra 2) write a polynomial function of least degree with integral coefficients that has the given zeros.

Please show the steps and explain!!

Answer 1

`x^(2) -2ix+3=0` .

Explanation:

Given the zeroes of the polynomial are

a=-i . and b=3i

The recquired polynomial is
`(x-a)(x-b)=0`

On substituting the values of a and b we get

`(x+i)(x-3i)=0`

`x^(2) -3xi+ix-3i^(2)=0`

`x^(2) -2ix+3=0` . (∵
`i^(2)=-1`)