Question

find all the roots of x^5 - 3x^4 + 3x^3 - 5x^2 +12 = 0

Answer 1

so far I got -1 and 2

Answer 2

but I think since the highest exponent is x^5, I have to have 5 answers...

Answer 3

Are you in algebra or calculus?

Answer 4

calculus

Answer 5

pre-calc

Answer 6

Maybe polynomial long division. You know -1 and 2 are roots, so two of factors are (x + 1) and (x - 2).

Answer 7

i did that and got it down to x^3 - 2x^2 + 3x -6...what do I do next?

Answer 8

If you plug x = 2 into your new equation, you find it equals 0 again, which means the power on the (x - 2) is 2. Try dividing by (x - 2) again.

Answer 9

ok, divide what though

Answer 10

x^3 - 2x^2 + 3x -6 divided by x - 3

Answer 11

Sorry, typo.

x^3 - 2x^2 + 3x -6 divided by x - 2

Answer 12

no doesn't work, I don't get 0 as my remainder

Answer 13

Hmm... it has be a while

Answer 14

ok, yea I'm so confused :)

Answer 15

When I divide using synthetic division, I get a remainder of 0.

Answer 16

using -2?

Answer 17

Positive 2. Synthetic division works with the actual root, not the factor. So +2 as opposed to the -2 in x - 2.

Answer 18

yes i know, I got 0 as well, but I still only got 2 answers and i need a total of 5

Answer 19

so far i got -1 and 2 as my answers but how do i find the other ones?

Answer 20

Really what you have gotten is -1, 2, and 2. Even though it is the same number, it is significant you were able to pull one factor out one and 2 was still a factor.