simple a maths inequalites

From the given condition, △ < 0

( - 2 )^2 - 4 ( k )( k ) < 0

4 - 4k^2 < 0

4 < 4k^2

k^2 > 1

k^2 - 1 > 0

( k + 1 )( k - 1 ) > 0

k < - 1 or k > 1


2007-07-26 16:27:24 補充：
Sorry, something more, as k &gt; 0 , so it should be k &gt; 1

2007-07-26 16:38:17 補充：
k should be &gt; 0 as the curve opens upwards. kx^2-2x+k &gt; 0 for all real values of x means the curve does not interest / touch the x-axis for all real values of x. So it means kx^2 - 2x + k = 0 has no real solutions and hence delta &lt; 0

kx^2 - 2x + k &gt; 0
(-2)^2 - 4(k)(k) &lt; 0
4 - 4k^2 &lt; 0
1 - k^2 &lt; 0
(1 + k) (1 - k) &lt; 0
-1 &lt; k &lt; 1