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.
+285 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
+240 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
