Question

Can someone help me please, I have to solve this equation using, foil, Fundamental Theorem of Algebra, the Rational Root Theorem, Descartes' Rule of Signs, and the Factor Theorem. 495=(x-2)(x-6)x

Answer 1

well first multiply it all out and set it equal to 0

Answer 2

Ok I got 0=(x^2-8x+12)x

Answer 3

where did the 495 go?
also distribute the x

Answer 4

x^3-8x^2+12x=495

Answer 5

make the right side 0 by subtracting by 495

Answer 6

ok so I'd get x^3-8x^2+12x=0

Answer 7

x^3 -8x^2 +12x -495 = 0

Answer 8

oh ok

Answer 9

then use Descartes Thm to determine how many pos and neg roots

or graph it on a calculator to guess any rational roots :)

Answer 10

I don't know how to do that :/

Answer 11

http://www.wolframalpha.com/input/?i=plot+x^3-8x^2%2B12x-495+

Answer 12

Thank you!

Answer 13

this shows there is 1 positive rational root

looks like its 11
verify by trying to see if (x-11) factors out

use synthetic division

11 | 1 -8 12 -495
_______________________
1

you do the rest and see if remainder is 0

Answer 14

yes it is

Answer 15

ok good , but the fundamental thm of algebra says we must have 3 roots because its a "x^3" function
to find the other 2 roots, use quadratic formula

Answer 16

ok I got +1 and -1

Answer 17

no please show work, what quadratic equation did you use?

Answer 18

http://www.purplemath.com/modules/quads/qform01.gif

Answer 19

you should have this:

11 | 1 -8 12 -495
11 33 495
------------------
1 3 45 0

--> (x-11)(x^2 +3x +45) = 0

Answer 20

sorry the link doesn't work

Answer 21

I did have that

Answer 22

\[x = \frac{-3 \pm \sqrt{9-4(1)(45)}}{2}\]

Answer 23

ok I got -28.5
-171 under the division sign
then divide it by 2 and I got -85.5
then divide -85.5 by -3 and 3

Answer 24

ahh, ok you can't divide by 2 because the "-171" is inside the radical

\[x = \frac{-3 \pm \sqrt{-171}}{2}\]

Answer 25

ok

Answer 26

whenever you have a neg num inside sqrt.....you get an imaginary number
\[x = \frac{-3 \pm i \sqrt{171}}{2}\]
simplify radical .... 171 = 19*9
\[x = \frac{-3 \pm 3\sqrt{19} i}{2}\]

Answer 27

ok, so would that be the answer?

Answer 28

yes those are the 2 complex roots and the 1 real root is 11

Answer 29

Ok Thank you