Factoring pm^3 + m^2 +pm +1, approximate roots...?

[Me_self]

1. the straight line 2x-3y+6=0 i reflected in the line y= -x find the equation of the reflection image
i dont know what to do for this.. i think is reflected in the y axis but i dont know about the equation :S

2. factor pm^3 + m^2 +pm +1

3.graph 3x^4 -15x^2+12 and label approximate roots if possible..

please help.. thx in advance.. =D

 

[soroban]

Re: Factoring , approx roots...?

Hello, Me_self!

1. The straight line \(\displaystyle 2x-3y+6\:=\:0\) is reflected in the line \(\displaystyle y= -x\)
Find the equation of the reflection image

Replace \(\displaystyle x\) with \(\displaystyle \text{-}y\).
Replace \(\displaystyle y\) with \(\displaystyle \text{-}x\).

\(\displaystyle \text{We have: }\;2x \;\;- \;\;3y -6\:=\:0\)
. . . . . . . .\(\displaystyle \downarrow\qquad\quad\downarrow\)
. . . . . . \(\displaystyle 2(\text{-}y) - 3(\text{-}x) -6\:=\:0 \quad\Rightarrow\quad 3x - 2y + 6 \:=\:0\)

2. Factor: .\(\displaystyle pm^3 + m^2 + pm + 1\)

\(\displaystyle \text{Factor: }\:m^2(pm+1) + (pm+1)\)

\(\displaystyle \text{Factor: }\pm+1)(m^2+1)\)

\(\displaystyle \text{3. Graph: }\:y \:=\:3x^4 - 15x^2 + 12\:\text{ and label approximate roots if possible.}\)

This is a quartic function, shaped like a "W".

\(\displaystyle \text{Find the }x\text{-intercepts: }\:3x^4 - 15x^2 + 12 \:=\:0 \quad\Rightarrow\quad 3(x^4 - 5x^2 + 4) \:=\:0 \quad\Rightarrow\quad 3(x^2-1)(x^2-4) \:=\:0\)

. . \(\displaystyle 3(x-1)(x+1)(x-2)(x+2) \:=\:0 \quad\Rightarrow\quad x \:=\:\pm1,\:\pm2\)


The graph looks like this . . .

                      |
   *                  |                  *
                      |
                      |
    *                 *                 * 
                   *  |  *
     *           *    |    *           *
  - - o - - - - o - - + - - o - - - - o - - -
     -2 *     *-1     |     1 *     *
           *          |          *
                      |

 

[Me_self]

Re: Factoring , approx roots...?

thank you so much soroban.. now i get it.. :mrgreen:

 

[mmm4444bot]

... now i get it.

I wonder.

I reviewed your posts at this site. You made one good attempt to explain what you're thinking, but, mostly, others are doing your work for you.

Next time, please try again to explain your reasoning and show some work.

 

[Me_self]

Re:

... now i get it.

I wonder.

I reviewed your posts at this site. You made one good attempt to explain what you're thinking, but, mostly, others are doing your work for you.

Next time, please try again to explain your reasoning and show some work.

how am i supossed to show my work here? :| if u teach me ill do it..

 

[stapel]

how am i supossed to show my work here?

You can use LaTeX, as the helpers have, by following the instructions provided in the "Forum Help" pull-down menu at the top of every forum page. Or you can use standard web-safe formatting.



Eliz.