Question

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

7, -11, and 2 + 6i

f(x) = x4 - 53x2 + 468x - 3080

f(x) = x4 - 9x3 - 42x2 + 234x - 3080

f(x) = x4 - 117x2 + 468x - 3080

f(x) = x4 - 9x3 + 42x2 - 234x + 3080
i really need help understanding this one

Answer 1

create a set of products by subtracting x from the given zeros

Answer 2

the complex zero has an extra root that tags along with it so dont forget to bring it along

Answer 3

and how do i do that

Answer 4

(a+bi) <--> (a-bi)

complex zeros come in pairs; and the only difference in their appearance is a change in operator

Answer 5

zeros are: 7, -11, 2 + 6i, 2 - 6i

subtract and x from each zero

7-x, -11-x, 2 + 6i-x, 2 - 6i-x

and multiply them all together

(7-x)(-11-x)(2 + 6i-x)(2 - 6i-x)

Answer 6

ok thank you

Answer 7

youre welcome

if you wanna double chk your work ....

http://www.wolframalpha.com/input/?i=%287-x%29%28-11-x%29%282+%2B+6i-x%29%282+-+6i-x%29