# Naughty Functions

Algebra Level 3

A parabolic curve $$f(x)=x^{2}+ax+2$$ has $$2$$ intersections with segment $$MN$$, with $$M(0,1)$$, $$N(2,3)$$.

All values of $$a$$ that make the statement given true can be expressed as $$-\frac{m}{n}\leq{a}<-p$$, with $$m$$, $$n$$ and $$p$$ positive integers and $$m$$ and $$n$$ coprime.

Evaluate $m+n+p$

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