SOLUTION: Find the value(s) of k for which the equation 3x^2-(k+1)x+k-2=0 has one real double root

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Question 831305: Find the value(s) of k for which the equation 3x^2-(k+1)x+k-2=0 has one real double root
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
Find the value(s) of k for which the equation 3x%5E2-%28k%2B1%29x%2Bk-2=0 has one real double root
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A:
The quadratic equation ax%5E2+%2B+bx+%2B+c+=+0,a ≠ 0, has one real double root if the discriminant b%5E2+-+4ac is equal to zero.
In 3x%5E2-%28k%2B1%29x%2Bk-2=0, a = 3, b = -(k + 1), and c = k - 2
b%5E2+-+4ac+ = %28-1%29%5E2%28k+%2B+1%29%5E2+-+%284%29%283%29%28k+-+2%29
=k%5E2+%2B+2k+%2B+1+-+12k+%2B+24
=k%5E2+-+10k+%2B+25, equate to zero
k%5E2+-+10k+%2B+25+=+0
%28k+-+5%29%5E2+=+0
Therefore, highlight%28k+=+5%29