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# Discriminant usage!!! watch

1. The equation x^"+5kx+2k=0, where k is a constant, has real roots.

(a) Prove that k(25k-8) is greater than or equal to 0. (done this, see below)

(b) Hence find the set of possible values of k

(c) Write down the values of k for which the equation x^2+5kx+2k=0 has EQUAL roots.

Part a-

b^2 is greater than 4ac
therefore 25k^2 is greater than or equal to 8k
therefore, once factorised, you get k(25k-8) is greater than or equal to zero.
2. You have k(25k-8)>=0, so find the values of k that make this inequality true. For part (c) you want b^2 = 4ac.
3. Well can't do part (b). Any hints? I have k is greater than 8/25, not sure if this is correct?- and don't know how to get the other limiting value.
Thanks
4. (Original post by Lawbutwhere?)
Well can't do part (b). Any hints? I have k is greater than 8/25, not sure if this is correct?- and don't know how to get the other limiting value.
Thanks
k>=8/25 or k=<0

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Updated: April 10, 2006
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