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discriminant question in homework - HSN forum

# discriminant question in homework

### #1craig1e

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Posted 14 January 2007 - 03:32 PM

I have to show that (1-2k)x^2-5kx-2k=0 has real roots for all integer values of k. I think all you have to do is find the discriminant and then make it a square but I couldn't get it to simplify. Can anyone help?

### #2Untouchable

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Posted 16 January 2007 - 12:27 AM

For (1-2k)x -5kx-2k=0 to have real roots the discriminant 0 (i.e. positive)

b - 4ac a = 1-2k b = -5k and c = -2k
(-5k) - (4 x (1-2k) x (-2k))
25k -(-8k + 16k )
25k + 8k - 16k
9k + 8k

9k will always be positive and 8k < 9k
9k + 8k will always be positive
discriminant 0
(1-2k)x 5kx-2k=0 has real roots for all integer values of k

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