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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