- #1
songoku
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Homework Statement
For a constant k, consider the function f(x) = x2 + kx + k2 - 2k - 4
Find the range of k for which f(x) = 0 has one solution between 0 and 1 and the other solution between 1 and 2
Homework Equations
quadratic formula
discriminant
The Attempt at a Solution
x2 + kx + k2 - 2k - 4 = 0
Using quadratic formula:
[tex]x=\frac{-k±\sqrt{-3k^2+8k+16}}{2}[/tex]
Then I set:
[tex]0 < \frac{-k-\sqrt{-3k^2+8k+16}}{2} < 1[/tex] and [tex]1 < \frac{-k+\sqrt{-3k^2+8k+16}}{2} < 2[/tex]
Am I on the right track? I think solving that inequality will take a lot of work... Is there other method?
Thanks