Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -14, and 5 + 8i

Answer 1

with real coefficients means if the polynomial has complex roots, they come in complex conjugate pairs. Because you have the root 5 + 8 i you will also need the complex conjugate. any idea what it is ?

Answer 2

yeah! i got as far as (x-4)(x+14)(x-(5-8i))(x-(5+8i))

Answer 3

the only thing is that i don't know how to distribute the 5-8i and 5+8i

Answer 4

I would first multiply out the complex part... it becomes real
x-(5-8i) = x-5 + 8i
and x - (5+8i) = x -5 -8i after we distribute the -1.
if we put in parens
( (x-5) + 8i ) * ( (x-5) - 8i)
this is like (a+b) (a -b) = a^2 - b^2 (fixed typo)
in this problem a is (x-5) and b is 8i
can you finish this part ?

Answer 5

so it would be (8ix - 40i) (-8ix + 40i)?