Given a quadratic equation $(x)=2x^2 -4kx+3k^2+5$, where $ k$ is a constant. I want to find out if the equation intersects the X-axis by measuring the delta, which is equal to $-8k^2-40$
Then I conclude that there are intersections if $k$ is between $-5$ to $ 5$ as delta becomes non-negative value.
However, when I put the function in a graph calculator, it turns out there is no roots for $y=0$ no matter how I change the value of $ k$. What wrong with my calculation and how can I prove that the function has no intersections with the X-axis ?
-8^2-40 is always negative.So given quadratic equation has no real solutions.Therefore it has no intersection with X-axis.