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

@surjithayer yay you're still on! can you help me? c:

Answer 2

complex roots always occur in pairs

Answer 3

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

Answer 4

x=5+4i
other root is 5-4i

Answer 5

Multiply and you get your polynomial

Answer 6

wait how do i multiply all that? ◑.◑

Answer 7

http://www.wolframalpha.com/input/?i=expand+%28x-3%29%28x%2B13%29%28x-5-4i%29%28x-5%2B4i%29

Answer 8

\[
(x-3) (x+13) (x-5-4 i) (x-5+4 i)=x^4-98 x^2+800 x-1599
\]

Answer 9

but HOW did you get that .-.

Answer 10

{(x-5)+4i}{(x-5)+4i}=(x-5)^2-(4i)^2

Answer 11

i^2=-1

Answer 12

youre speaking a different language sir

Answer 13

i am not speaking a different language.
(x-5)^2-16i^2=x^2-10x+25+16
=x^2-10x+41
i only solved complex part.
now you get
(x-3)(x+13)(x^2-10x+41)
now you can multiply

Answer 14

correction i have written wrong above.
it should be {x-5+4i}{x-5-4I}
={(x-5)+4i}{(x-5)-4i}

Answer 15

so x^3-13x^2+71x-123 and then i multiply it all by x+13?

Answer 16

okay i got it ^.^ thank you!

Answer 17

yw