Question

Can somebody show me how to work this out? x^3-2x^2+3x+10=0

Answer 1

So you need to find the roots?

Answer 2

Yes ma'am @raechelvictoria

Answer 3

So far I found the factors of 10 and x^3. Am I headed in the right direction?

Answer 4

Yes. Then substitute those values into the equation until you the equation will equal to zerio (remainder theorem)

Answer 5

I couldn't find a number that balanced it out. Maybe I messed up on the math. I will try again.

Answer 6

Hmm it turns out the real root is x = -1.3387.
Are you sure you posted the equation correctly?

Answer 7

I'm dumb I posted the wrong thing. Here is the original equation: q(x)=x^4-4x^3+x^2+16x-20. That other equation was after synth div

Answer 8

When 2 was under the bracket. Where do I go from there?

Answer 9

Oh so you already found 2 to be a root?
That looks correct.
Maybe you made a boo boo when you did the division, lemme check.

Answer 10

Synthetic Division is giving me: x^3 - 2x^2 `- 3x` + 10 = 0

See the minus on the 3x?
Maybe you made a small error right there.

Answer 11

Indeed. Thank you for catching that. What next?

Answer 12

So you took the factors of your constant and divided them by the factors of your leading coefficient. That gave you possible rational roots.

You'll need to check them again :c grr
Hint hint: Check 2 and -2 again. One of those should work out.

Answer 13

I'm confused what you mean I need to check them again?

Answer 14

I see what you mean @zepdrix -2 did work so now I'm going to use the quad formula. Thanks for all the help!

Answer 15

I ended up with roots of -2,2,2+i, and 2-i

Answer 16

Ah good job! :)

Answer 17

This is another one I'm going to work on g(x)=x^6-1. So would I do the same steps?

Answer 18

For g(x) we can write it as the `difference of squares`.

x^6 = (x^3)^2
1 = 1^2

x^6 - 1 = (x^3)^2 - 1^2

Do you remember how to factor the difference of squares?
They break down into `conjugates`.

Answer 19

No I don't remember how to do that.

Answer 20

Difference of squares break down into factors like this:

a^2 - b^2 = (a-b)(a+b)

So in our problem, it would factor down to:

(x^3 - 1)(x^3 + 1)

Answer 21

I ended up doing syth division, but that other way is quicker.

Answer 22

Oh synthetic worked on this one? cool

Answer 23

So here are my final roots 1,-1, -1+-iSqrt(3)/2, and 1+-isqrt(3)/2. Does this look right?

Answer 24

Ya that's what I'm getting also.

Answer 25

Alright, thanks again for helping me out!

Answer 26

Refer to the Mathematica calculation.

Answer 27

Thank you both @robtobey @zepdrix

Answer 28

Your welcome. You might be interested in the following video.

http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html