Question

FACTORING:

314x^3+1256x^2-7536

in order to solve using discriminate formula(b^2-4ac)?

Answer 1

you sure you dont mean

314x^2+1256x-7536 ?

Answer 2

nooo

Answer 3

well
314x^3+1256x^2 +0x -7536
a x^3 +b x^2 + cx +d

x^2 (a x+b)+d

maybe that helps

Answer 4

x^2 (314 x+1256)-7536

Answer 5

could help.

Answer 6

That's confusing, I'm just gonna give up, find another method

Answer 7

it seems fishy cuzz (b^2-4ac) applies to second degree polynomials. Not 3rd.

Unless i am missing something.

Answer 8

then maybe it should be 314x^2+1256x-7536, even though I was pretty sure I combined them right

Answer 9

lol maybe.

the discriminant for a that cubic function in standard form is

b^2 c^2-4 a c^3-4 b^3 d+18 a b c d-27 a^2 d^2

:O

Answer 10

or since you got no coeeficient in the x term

-d (27 a^2 d+4 b^3)

Answer 11

I'm not sure that's the result I'm looking for

Answer 12

http://www.wolframalpha.com/input/?i=314x%5E3%2B1256x%5E2-7536

Answer 13

314 (x-2) (x^2+6 x+12)
( this )
ooh ^

now you can do discriminant :D

Answer 14

ohh that's factored? or...

Answer 15

that is
314x^3+1256x^2-7536
factored to
314 (x-2) (x^2+6 x+12)

You can apply the discriminant to (x^2+6 x+12) but idk what for lol

Answer 16

I was told to use the discriminant to find out the zeros by fundamental theorem?

Answer 17

Can you give the original problem in the way it was originally stated?

Answer 18

Option 1 - Cylinder

You will need the following materials to find the volume of a cylinder:

A cylindrical object such as a soup can or thermos
Ruler or tape measure
Graphing technology (e.g., graphing calculator or GeoGebra)
Procedure:

Measure and record the diameter and height of the cylindrical object you have chosen in inches. Round to the nearest whole number.

Apply the formula of a right circular cylinder (V = r2h) to find the volume of the object. (Note: Be sure to find the radius from the diameter measurement by dividing by 2.)

Now suppose you knew the volume of this object and the relation of the height to the radius, but did not know the radius. Rewriting the equation with one variable would result in a polynomial equation that you could solve to find the radius.

Rewrite the formula using the variable x for the radius. Substitute the value of the volume found in step 2 for V and express the height of the object in terms of x plus or minus a constant. For example, if the height measurement is 4 inches longer than the radius, then the expression for the height will be (x + 4).

Simplify the equation and write it in standard form. Multiply each term in the equation by 100 to eliminate any decimals, if necessary.
Find the solutions to this equation algebraically using the Fundamental Theorem of Algebra, the Rational Root Theorem, Descartes' Rule of Signs, and the Factor Theorem.

Answer 19

314x^3+1256x^2-7536 First of all getting this factored is a pain in the butt.
but since i gave it to you it's the following
314 (x-2) (x^2+6 x+12)
^ 314 dont matter
^ x-2=0 means solving for x will give you 2 as a root
^ (x^2+6 x+12) part...
(x^2+6 x+12) you apply discriminant.
a b c
(b^2-4ac)

plug in numbers
6^2-4(1)(12)
36-4*12
36-48=-12 is discriminant .

If i remember right if D <0 then it has imaginary zeros.

Answer 20

Okay what were the height, radius, and volume?

Answer 21

h=6, d=4, r=2, v=75.36

Answer 22

Okay, cool. So then, we're supposed to assume we don't know the radius or the height. We just know that
r = h-4
and that volume = 75.36

Answer 23

Does that much make sense to you?

Answer 24

I thought the h=x+4 ?

Answer 25

Yes. That's equivalent.

Answer 26

yes and I after putting it all together and simplifying I got 314x^3+1256x^2-7536=0 ?

Answer 27

Oh, you're taking out all of the decimals.

Answer 28

yeah to make life easier

Answer 29

Haha I tend to think that makes life a good bit harder. You know, since 314 is a much different number than 3.14.

Answer 30

What are you suggesting?

Answer 31

after working on this for two hours I'm sure my answer should come from 314(x-2)(x^2+6x+12) ?

Answer 32

not if you made 3.14 into 314

Answer 33

I see what she did. She just multiplied the whole equation by 100.

Answer 34

is there a difference in the end? even the directions instructed that I get rid of all demcials

Answer 35

Yeah, there's no problem with it. It was just confusing because I didn't realize what you were doing.

Answer 36

Factor out a GCF of 314 to get:

\(\Large 314(x^3 + 4x^2 + 24) = 0\)

Answer 37

And that factors from there the way you had it.

\(\Large 314(x-2)(x^2+6x+12) =0\)

From the first factor, (x-2) you get what root?

Answer 38

To get the roots that go along with a single factor, set the factor equal to 0 and solve for x.

Answer 39

I wouldn't use discriminant at all??

Answer 40

No. Once a polynomial is factored, you can find the solutions by setting each factor equal to 0. Let me show you an example.

\(\Large (x+4)(x-1)(x^2+x+20) = 0\)
x+4 =0
gives me x=-4
x-1 = 0
gives me x=1
\(\large x^2 + x +20 =0\)
I need to use the quadratic formula for this one, and I get 2 imaginary solutions.