Question

Write a polynomial function with rational coefficients so that p(x) = 0 has the given roots. 5, 2i

Answer 1

please don't spam your questions bro :) someone will come to your aid :)

Answer 2

you can ask it once and then ask for help in the chat and paste the link there ;) that's better and we'll all be happy :D

Answer 3

where's the chat?

Answer 4

it's down the page there and it should be an orange color at the moment if you haven't clicked it yet... "Mathematics"

Answer 5

in any case if a polynomial has roots 5 and 2i, it means that you should have something like
(x-5)(x-2i)=0 when you factorize it, so you expand that and you should have the polynomial function :)

Answer 6

How would I expand it?

Answer 7

i will be there in a while but jorgeeeee here's how to expand it
(x-5)(x-2i)=0
x(x-2i)-5(x-2i)=0
then use the distributive property to expand it :) let me know if you can't do that too, i'll help you with it :)

Answer 8

x(x-2i)-5(x-2i)=0
so, that would be (x-5)(x-2i)^2 ?

Answer 9

nooo lol ok i'll teach you
\(\huge a(b+c)=ab+ac \)
so with what we have here, you'll have something like this
\[\huge (x-5)(x-2i)=0 \]\[\huge x(x-2i)-5(x-2i)=0 \] then we'll apply the first rule here
\[\huge (x^2-x(2i))-(5x-5(2i))=0 \]\[\huge x^2-2xi-5x+10i=0 \]
do you understand it up to this point?

Answer 10

What rule did you exactly apply? you're multiplying?

Answer 11

i'm multiplying yes but this is the distributive property :)

Answer 12

So you always set it up the opposite way like (x+ or - and the number) then use the second one twice?