How do i write a polynomial function of least degree with intergral coefficients that has the given zeros. the zeros are 3i and 2-i

Question

My son is in an algebra 2 class in public HS in CA.  Thanks for your help

Answer 1

Russ, if the zeroes were 2 and 3, then x = 2 and x = 3.  We expand that as x - 2 = 0 and x - 3 = 0.

 

We further expand that into (x-2)(x-3) = 0.  Multiply out to get x² - 2x - 3x + 6 = 0.  Combine like terms for x - 5x +6 = 0.

 

Let's skip a step.  (x - 3i)(x - (2-i)) = 0.  x² - 3ix - 2x + ix +6i + 3i² = 0

 

Remember that i = the square root of -1.  The square root of "anything" squared is "anything."

 

i² = -1, so we have x² - 2ix - 2x - 3 = 0.

 

x² - 2x(i- 1) - 3 =0.

 

Hope this helps!