Does "Real Values" in part ii means that the numbers must be more than or equal to 0?
I don't know how to do the part ii.
The equation of a curve is
i) Find the range of values of k if the curve does not meet the x-axis.
ii) Show that the line intersects the curve for all real values of k.
Solution
i) Since curve does not meet x-axis,
k < 0 or 4k < 16
k < 4
Range of Values of k is k < 4
ii) Stucked!
Observe:
We like to find out for wich k the following equation has solutions:
This equation has real solutions if:
It's not hard to see that D > 0 for all real k.
No it means the numbers are not complex, that is of the form a+biDoes "Real Values" in part ii means that the numbers must be more than or equal to 0?
where
Ofcourse it's not fully sufficient, but a simple argument is:What you have written is not sufficient to say that the Discriminant is always nonnegative
has no real solutions
since
Therefore by continuity of we have or for all k.
Since for all negative k we have it must be the first case.