Question

HELP PLEASE! METAL.
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -14, and 5 + 8i

f(x) = x4 - 362.5x2 + 1450x - 4984
f(x) = x4 - 9x3 + 32x2 - 725x + 4984
f(x) = x4 - 67x2 + 1450x - 4984
f(x) = x4 - 9x3 - 32x2 + 725x - 4984

Answer 1

\[(x-4)(x+14)\] is part of it

Answer 2

how do you know johnny? that's my BF.

Answer 3

then find the quadartic with zeros \(5+8u,5-8i\)

Answer 4

srry off topic.

Answer 5

heeeere's johnny!

Answer 6

Lol.

Answer 7

the quadratic with zeros \(a+bi\) is \(x^2-2ax+a^2+b^2\)

Answer 8

so the quadratic with zeros \(5+8i\) is
\[x^2-10x+5^2+8^2\]

Answer 9

your really good at this.

Answer 10

or
\[x^2-10x+89\]

Answer 11

i can show you why that is true if you like, or you can believe me
thank you btw

Answer 12

that's not an answer choice.

Answer 13

final job
\[(x-4)(x+14)(x^2-10x+89)\] which pretty much is a recipe for failure, use technology

Answer 14

lol yeah because you were not even close to done!

Answer 15

ok

Answer 16

ugh...

Answer 17

oh not it is real real easy
watch

Answer 18

http://www.wolframalpha.com/input/?i=%28x-4%29%28x%2B14%29%28x^2-10x%2B89%29

Answer 19

tada
you can even check that it has the right zeros if you scroll down

Answer 20

Noo way... your awesome.

Answer 21

(blush)

Answer 22

wait...

Answer 23

,,,

Answer 24

Give an example of a rational function that has a horizontal asymptote of y = 2/9.

Answer 25

just make the leading coefficient of the numerator 2, the denominator 9 and make sure the degrees are the same
you want a simple example you can say
\[f(x)=\frac{2x}{9x+1}\]

Answer 26

Write a linear factorization of the function.
f(x) = x4 + 16x2

Answer 27

but you could say \[f(x)=\frac{2x^2-5x+4}{9x^2+3x-2}\] or whatever

Answer 28

lol what am i the askit casket?

Answer 29

Your like a genius, I have to ask... :)

Answer 30

factor out the \(x^2\) and get
\[f(x)=x^2(x^2+16)\] then if you want to factor over the complex numbers solve \(x^2+16=0\) get \(x=\pm 4i\) and so
\[x\times x\times (x+4i)(x-4i)\] is your linear factorig

Answer 31

Use the Rational Zeros Theorem to write a list of all potential rational zeros

f(x) = x3 - 10x2 + 4x - 24

+/-1, +/-2, +/-3, +/-4, +/-6, +/-8, +/-12, +/-24
+-/-1, +/-One divided by two., +/-2, +/-3, +/-4, +/-6, +/-8, +/-12, +/-24
+/-1, +/-2, +/-3, +/-4, +/-24
+/-1, +/-2, +/-3, +/-4, +/-6, +/-12, +/-24

Answer 32

this one is for you
list ALL factors of 24

Answer 33

which i think is the first one but you can check

Answer 34

answer choice 4 then.

Answer 35

i mean 1

Answer 36

no answer choice 4 is missing 8

Answer 37

very tricky

Answer 38

yea so its 1 right?

Answer 39

yeah

Answer 40

ok, I appreciate you satellite one last question. give me one minute.

Answer 41

Choice #1: Describe each of the following properties of the graph of the Cosine Function, f(theta) = cos(theta) and relate the property to the unit circle definition of cosine.

Amplitude
Period
Domain
Range
x-intercepts

Answer 42

you want the amplitude of cosine?

Answer 43

that is 1, because cosine is the first coordinate on the unit circle, so goes from -1 to 1

Answer 44

what's listed... this is like an essay format type thing you know.

Answer 45

period of cosine is \(2\pi\) as that is the circumference of the unit circle

Answer 46

domain of cosine is all real numbers, you can take the cosine of anything

Answer 47

range is from -1 to 1, i.e. \[[-1,1]\]once again because it is a point on the unit circle given by \(a^2+b^2=1\) so the maximum is 1 and the minimum is -1

Answer 48

it crosses the x axis where the first coordinate on the unit circle is 0, namely at \[\frac{\pi}{2},\frac{3\pi}{2},...\]

Answer 49

if you want to be fancy you can say
\[n\pi-\frac{\pi}{2}\]

Answer 50

wow, so how are you soo good at this... curious.

Answer 51

i will let you pad it out with words to look like an essay
have fun
now i am going to go have a beer with johnny

Answer 52

if you continue to study math one day you will look at this and it will seem like \(3\times7\)

Answer 53

I'M A HUGE FAN, BYYE!!

Answer 54

ttyl

Answer 55

well I mean i'm not going anywhere, just waiting to see if you are...

Answer 56

I could do this all day.

Answer 57

State the horizontal asymptote of the rational function.
f(x) = quantity x squared plus nine x minus nine divided by quantity x minus nine.
y = 3
None
y = 9
y = -9