Find sum of all integral values of $a$ in $[1,100]$ for which the equation $x^2-(a-5)x+(a-15/4)=0$ has at least one root greater than zero.
I used the condition that discriminant must be greater than or equal to zero and obtained that $a \in [1,4] \cup [10,100]$, but I am not able to visualize the condition for 'at least one root greater than zero'. Please provide some insight.