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

Answer 1

in order to have real coefficients, all complex roots must appear as conjugates

Answer 2

do you know what the conjugate of 2+6i is?

Answer 3

no :(

Answer 4

-2-6i

Answer 5

http://www.mathsisfun.com/numbers/complex-numbers.html

a+bi and a-bi are complex conjugates

Answer 6

ohh ok

Answer 7

so 2-6i

Answer 8

yep
so can you write the polynomial in factored form?

Answer 9

7, -11, and 2 + 6i

Answer 10

no...

in factored form it would be something like this...

f(x) = (x-c)(x-d)(x-(a+bi))(x-(a-bi))

Answer 11

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

Answer 12

not quite...
the complex factor would be x-(2+6i) and you would need its conjugate as a factor also, if your polynomial is to have real coefficients

Answer 13

i don't really understand

Answer 14

if 4 is a root, it implies that f(4) = 0 and that the polynomial must have a factor of x-4, correct?

Answer 15

yes

Answer 16

so if 2+6i is a root, then x-(2+6i) is a factor. but if your polynomial is to have real coefficients then all complex roots must occur as complex conjugate pairs

Answer 17

so x-(2-6i) also must be a factor

Answer 18

once you have the factored form, just multiply out to get into standard form