Question

can anyone help me please in this precal question? write the polynomial in standard from
3,-13,and 5+4i.. please and thank you

Answer 1

start with
\[(x-3)(x+13)\] since that will give you the zeros of \(3\) and \(-13\)

Answer 2

then you have to multiply that by the quadratic that has zeros \(5+4i\) and \(5-4i\)
that one is not too hard to find
do you know how to do it?

Answer 3

i can show you if you like
two ways, one is easy the other is real real easy

Answer 4

yea can you show me the real easy way?

Answer 5

ok but first the easy way, because the real real easy way requires memorizing something

Answer 6

ok

Answer 7

start with
\[x=5+4i\]
and work backwards
subtract \(5\) and get
\[x-5=4i\] then square both sides (carefully) get
\[(x-5)^2=(4i)^2\\
x^2-10x+25=-16\] then add \(16\) and get
\[x^2-10x+41\] as your quadratic

Answer 8

that is the easy enough way, like solving a quadratic equation only backwards
the real real easy way (if you are going to do more than one of these) is to memorize that if
\[a+bi\] is a zero then the quadratic is
\[x^2-2ax+(a^2+b^2)\]

Answer 9

you had
\[5+4i\] so the quadratic was
\[x^2-2\times 5x+(5^2+4^2)=x^2-10x+41\]

Answer 10

final job is to multiply out
\[(x-3)(x+13)(x^2-10x+41)\] and again although this is annoying there is a real real easy way to do iot

Answer 11

namely cheat
http://www.wolframalpha.com/input/?i=%28x-3%29%28x%2B13%29%28x^2-10x%2B41%29

Answer 12

ok lemme try workin it out sorry all new to this stuff lol

Answer 13

ok thank you so much! I got it now

Answer 14

yw