Question

Please help! My assignment is due a minute before midnight tonight.

Find all the real zeros of the polynomial. Us the quadratic formula is necessary.
P(x) = 2x^3 - 10x^2 +4x +24

Evaluate the expression and write the result in the form of a+bi. (Simplify completely)
8-7i (over) 1-8i
(Last question is below)

Answer 1

A polynomial P is given.
P(x) = x^3 - 8
(a) Final all zeros of P, real and complex.
(b) Factor P completely.

Answer 2

we can do the last one fast

Answer 3

\[x^3-8=(x-2)(x^2+2x+4)\] because that is how you factor the difference of two cubes
evidently one zero is \(2\) the other two are found using the quadratic formula for
\[x^2+2x+4=0\] either that, or what is even easier, completing the square

Answer 4

you got that or you still need help
otherwise we can move on and do the first two

Answer 5

I got it but can you point out to me what the factored form is?

Answer 6

sure
once you get the zeros, which i believe are \(-1\pm\sqrt{3}i\) you factor as
\[(x-2)(x-(1+\sqrt3 i))(x-(1-\sqrt3 i))\]

Answer 7

Okay.

Answer 8

\[P(x) = 2x^3 - 10x^2 +4x +24\] solve \[P(x) = 2(x^3 - 5x^2 +2x +12)=0\]

Answer 9

by some miracle one of the zeros is 3, so this factors as \[2 (x-3) (x^2-2 x-4) = 0\]

Answer 10

Okay, I know 3 is one of the zeros.

Answer 11

use the quadratic formula or complete the square to find the zeros of \[x^2-2x-4=0\]

Answer 12

Sorry, internet running slow.

Answer 13

completing the square is easiest, think you get
\[x=1\pm\sqrt5\]

Answer 14

Yes.

Answer 15

ok so that one is done

Answer 16

For the last question we have left I have done it before but two different people, one telling me it's right and another telling me it's wrong and I'm confused. Let me put up what I did.

Answer 17

i have an idea, lets cheat

Answer 18

Huh?

Answer 19

http://www.wolframalpha.com/input/?i=%288-7i%29%2F%281%2B8i%29

Answer 20

i can show you how to do it, most modern calculators can

Answer 21

Ah, thank you.

Answer 22

\[\frac{8-7i}{1-8i}\frac{1+8i}{1+8i}=\frac{(8-7i)(1+8i)}{1^2+8^2}\]

Answer 23

almost midnight....

Answer 24

Umm... Can we go back to the first question we did? Webassign isn't taking the factored form.

Answer 25

which one?

Answer 26

The P(x) = x^3 - 8

Answer 27

if it does not like \[(x-2)(x-(1+\sqrt3 i))(x-(1-\sqrt3 i))\] try
\[(x-2)(x-1-\sqrt3)(x-1+\sqrt3)\]

Answer 28

and if it does not like that, then i am lost
#$%^& webassign

Answer 29

Alright. I thought webassign was the greatest thing at the beginning of the semester but I really hate with a Die Hard passion now.

Answer 30

it is just frustrating when it wants one syntax and you write another

Answer 31

Ah, I figured out what we did wrong.

Answer 32

what ?

Answer 33

We had \[(x-1-\sqrt{3}i)(x-1+\sqrt{3}i)\] instead of \[(x+1-\sqrt{3}i)(x+1+\sqrt{3}i)\]

Answer 34

doh crap

Answer 35

It's always the little things.

Answer 36

And with 9 minutes to spare, haha.

Answer 37

done?
great
time for me to reture

Answer 38

retire

Answer 39

Thank you for helping.

Answer 40

yw