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discriminant question in homework - HSN forum

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discriminant question in homework


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#1 craig1e

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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?

#2 Untouchable

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Posted 16 January 2007 - 12:27 AM

For (1-2k)x power2.gif -5kx-2k=0 to have real roots the discriminant greaterorequal.gif 0 (i.e. positive)

b power2.gif - 4ac a = 1-2k b = -5k and c = -2k
(-5k)power2.gif - (4 x (1-2k) x (-2k))
25k power2.gif -(-8k + 16k power2.gif )
25k power2.gif + 8k - 16k power2.gif
9k power2.gif + 8k

9k power2.gif will always be positive and 8k < 9k power2.gif
9k power2.gif + 8k will always be positive
discriminant greaterorequal.gif 0
(1-2k)x power2.gif 5kx-2k=0 has real roots for all integer values of k





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