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The equation

\(\frac{x}{x - 1} + \frac{x}{x+4} = kx\)

has exactly two complex roots. Find all possible complex values for  Enter all the possible values, separated by commas.

 
 Jan 10, 2021
 #1
avatar+312 
0

Multiply your equation  through  by    (x + 1) ( x + 2)

 

And we have that

 

2x + 3  =   k ( x^2  + 3x + 2)

 

2x + 3  =  kx^2  + 3kx  + 2k

 

kx^2   + (3k - 2)x  + (2k  -3)  =  0

 

For this to have complex roots.....the discriminant must  be <  0

 

So....

 

(3k - 2)^2  - 4 ( k) ( 2k -3)  <  0

 

9k^2  - 12k + 4   - 8k^2 + 12k  <  0

 

k^2  +  4   <  0    (1)

 

k^2  <  -4      take  both roots

 

k <  -2i         k > 2i

 

Any  value of  k < -2i  produces complex roots

And any value of k > 2i  produces  complex roots

 
 Jan 10, 2021
 #2
avatar+78 
0

Once again, you have stolen another person's work...

It is disrespectful and not really good. Just give the link

Here is the real answer: https://web2.0calc.com/questions/this-is-hard_6

 
DewdropDancer  Jan 11, 2021

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