SOLUTION: Determine the value of k when the equation has a repeated real solution: kx^2+(k+1)x-(k+2)

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Question 988562: Determine the value of k when the equation has a repeated real solution:
kx^2+(k+1)x-(k+2)

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Finish the description correctly. "...when the root of the EXPRESSION is repeated."

The variable being x, Use the discriminant.

kx%5E2%2B%28k%2B1%29x-%28k%2B2%29=0 for the equation.
Discriminant must also be zero, %28k%2B1%29%5E2-4%2Ak%28-1%29%28k%2B2%29=0.

%28k%2B1%29%5E2%2B4k%28k%2B2%29=0
k%5E2%2B2k%2B1%2B4k%5E2%2B8k=0
5k%5E2%2B10k%2B1=0
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k=%28-10%2B-+4sqrt%285%29%29%2F%282%2A5%29
highlight%28k=%28-5%2B-+2sqrt%285%29%29%2F5%29