+0  
 
0
83
5
avatar

 

find all the real rational zeros of x^4+x^3-11x^2+x-12

Guest Oct 13, 2017

Best Answer 

 #1
avatar+5553 
+1

First factor this.

 

x4 + x3 - 11x2 + x - 12     Rearrange.

 

x3 + x + x4 - 11x2 - 12       Factor  x  out of the first two terms and split the  -11x2 .

 

x(x2 + 1) + x4 + x2 - 12x2 - 12    Factor  x2 out of  x4 + x2     and  -12  out of  -12x2 - 12 .

 

x(x2 + 1) + x2(x2 + 1) - 12(x2 + 1)     Factor  (x2 + 1)  out of all the terms. 

 

(x2 + 1)(x2 + x - 12)    Factor the  x2 + x - 12 .

 

(x2 + 1)(x2 + 4x - 3x - 12)

 

(x2 + 1)(x(x + 4) - 3(x + 4))

 

(x2 + 1)(x + 4)(x - 3)

 

To find out the  x  values that make this equal to zero, set each factor equal to zero and solve for  x .

 

x2 + 1  =  0           x - 3  =  0           x + 4  =  0

x2  =  -1                 x  = 3                   x  =  -4

not real

hectictar  Oct 13, 2017
edited by hectictar  Oct 13, 2017
edited by hectictar  Oct 13, 2017
Sort: 

5+0 Answers

 #1
avatar+5553 
+1
Best Answer

First factor this.

 

x4 + x3 - 11x2 + x - 12     Rearrange.

 

x3 + x + x4 - 11x2 - 12       Factor  x  out of the first two terms and split the  -11x2 .

 

x(x2 + 1) + x4 + x2 - 12x2 - 12    Factor  x2 out of  x4 + x2     and  -12  out of  -12x2 - 12 .

 

x(x2 + 1) + x2(x2 + 1) - 12(x2 + 1)     Factor  (x2 + 1)  out of all the terms. 

 

(x2 + 1)(x2 + x - 12)    Factor the  x2 + x - 12 .

 

(x2 + 1)(x2 + 4x - 3x - 12)

 

(x2 + 1)(x(x + 4) - 3(x + 4))

 

(x2 + 1)(x + 4)(x - 3)

 

To find out the  x  values that make this equal to zero, set each factor equal to zero and solve for  x .

 

x2 + 1  =  0           x - 3  =  0           x + 4  =  0

x2  =  -1                 x  = 3                   x  =  -4

not real

hectictar  Oct 13, 2017
edited by hectictar  Oct 13, 2017
edited by hectictar  Oct 13, 2017
 #2
avatar+648 
+2

Wow, good job Hecticar. Certainy wouldn't haven't gotten that.

AdamTaurus  Oct 13, 2017
 #3
avatar+79827 
+1

I agree with AT.....that's a very nice factoring "trick,"  hectictar.....!!!

 

 

cool cool cool

CPhill  Oct 13, 2017
 #4
avatar+5553 
+1

Well thank you!  smiley

I did have a little hint after I saw what the answer was supposed to be from WolframAlpha though!!!

hectictar  Oct 13, 2017
 #5
avatar+79827 
+1

LOL!!!!!!.....some people might call that "cheating"....I prefer the term, "research"

 

 

cool cool cool

CPhill  Oct 13, 2017

18 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details