need some help with algebra 2

Question

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

 

3i, 2, and −2

Answer 1

Hi Juan,

First of all, when one of zeros is complex number you can be sure THE CONJUGATE OF THAT IS ALSO OTHER ZERO, so all zeros are

x =2 x = -2 x = 3i x= -3i

f(x) = (x - 2) (x + 2) ( x - 3i) (x + 3i)

f(x) = ( x^2 - 4) ( x^2 -9i^2)

f(x) = ( x^2 - 4) ( x^2 +9)

f(x) = x^4 + 5 x^2 -36

I hope it is useful,

Minoo