First question : First, you know that . That means that if you sketch the graph for any permitted value of , it will be a curved parabola open to the top. Therefore, there are only two possible situations : either it never touches the x-axis, therefore there are no real solutions and the equation is always positive, either it cuts the x-axis and there are solutions. But the equation cannot be all negative. Now, if , that means that . Basically, it means that the discriminant is negative, thus the equation admits no real solution and therefore is positive for all real (you got to rewrite it properly though, I gave you the idea).
Second question : you need to find all values of for which the given quadratic has only positive values (that is, has no real solution). Think of your equation like this :
Get the discriminant of this equation :
By substituting your values :
Now, what is the characteristic feature of a quadratic equation with no real solution (i.e. all values are positive, in our case) ? The discriminant is negative. Therefore you have :
Solve for and you will then have the range of when the quadratic equation has no real solution (always positive).
Does it help ? Ask if you still need help.
PS : why did you put a congruent sign ( ) on your function ?