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

the coefficients are 3 and -13?

Answer 2

@Josh_S I believe it says the zeros include those listed.

Answer 3

if 3 is a zero, then x-3 is a factor. If -13 is a zero then x+13 is a factor. If 5+4i is a zero than x-(5+4i) is a factor. If 5+4i is a zero then 5-4i is also a zero and hence x-(5-4i) if a factor.

Answer 4

thats how you do it, i was thinking, i havent done those in awhile lol

Answer 5

create a set of products by subtracting x from the given zeros
the complex zero has an extra root that tags along with it so dont forget to bring it along
(a+bi) <--> (a-bi)

complex zeros come in pairs; and the only difference in their appearance is a change in operator
zeros are: 3, -13, 5 + 4i, 5 - 4i

subtract and x from each zero

3-x, -13-x, 5 + 4i-x, 5 - 4i-x

and multiply them all together

(3-x)(-13-x)(5 + 4i-x)(5- 4i-x)

if you wanna double chk your work ....
http://www.wolframalpha.com/input/?i=%283-x%29%28-13-x%29%285+%2B+4i-x%29%285-+4i-x%29

Answer 6

if correct please click best response.