1Offcourse you can do it that way.
When you combine both the things, you get af(k)>0
which means either a>0, f(k)>0 or a<0, f(k)<0
when we say the confition for a number k to be greater than both the roots of ax2+bx+c (whether a is less or greater than 0), one of the conditions is af(k)>0.
Why do we multiply a with f(k) and why not simply check whether f(x) is > 0 for a>0 and less than 0 for a<0
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