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What is the sum of the x-values that satisfy the equation  5 = (x^3 - 2x^2 - 8x)/(x + 2) + 5/(x + 2) - 11x/(x + 2)?

 Apr 12, 2022
 #1
avatar+124592 
+2

So  we have

 

5  =   [ x^3 -2x^2 - 8x   ] / [ x + 2]  +  5 / [x + 2]  -  [11x]  / [x + 2]

 

Multiply through by  x + 2

 

5 (x + 2)  = [x^3 -2x^2 -8x ]   + 5  - 11x

 

5x + 10  = x^3 -2x^2 - 19x + 5

 

x^3 - 2x^2 - 24x - 5   =   0

 

We have the form

 

ax^3  + bx^2 + cx  + d = 0

 

By Vieta......the sum of the x values  that  satisfy  this  =  (-b) / a  =     - (-2) / 1  =  2

 

cool cool cool

 Apr 12, 2022
 #2
avatar+114 
-2

Smarty

 

coolcoolcool

 Apr 12, 2022

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