SOLUTION: Find the values of k so that the equation {{{(k-2)x^2+4x-2k+1=0}}} has two distinct real roots.

Algebra ->  Functions -> SOLUTION: Find the values of k so that the equation {{{(k-2)x^2+4x-2k+1=0}}} has two distinct real roots.      Log On


   

Question 979446: Find the values of k so that the equation %28k-2%29x%5E2%2B4x-2k%2B1=0 has two distinct real roots.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant must be positive.

b%5E2-4ac%3E0

4%5E2-4%28k-2%29%281-2k%29%3E0

16-4%28k-2-2k%5E2%2B4k%29%3E0

16-4%285k-2-2k%5E2%29%3E0

16-20k%2B8%2B8k%5E2%3E0

8k%5E2-20k%2B24%3E0

2k%5E2-5k%2B6%3E0------solve this inequality.