Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

3, -13, and 5 + 4i

Answer 1

if 'a' is the zero of f(x) then (x-a) is the factor
so can u list the factors ?

Answer 2

uhh, no? factors of 5+4i?

Answer 3

no, example, if 3,2 are zeros of f(x) then the function is (x-2)(x-3)

Answer 4

oh, so its (x-3) (x+13) ?

Answer 5

and what about complex zeros ?

Answer 6

the 5+4i? (x-5) (x-4i) ?

Answer 7

hint :
if a+bi is a zero, then a-bi is also a zero of a function with real co-eff

Answer 8

no, not like that

Answer 9

im confused

Answer 10

ok, 5+4i is a zero, then 5-4i is also a zero of the function
hence the factors are
(x-(5+4i)) (x-(5-4i))
got this ?

Answer 11

alright

Answer 12

so result proceeds:)