Is it a root, or not?

Algebra Level 5

\[\large -400{ x }^{ 5 }+2660{ x }^{ 4 }-3602{ x }^{ 3 }+1510{ x }^{ 2 }+18x-90\]

The polynomial above has five rational roots. Suppose you guess a rational number which could possibly be a root (according to rational root theorem), what is the probability that it actually is a root?

If your answer is \( \frac ab\) for coprime positive integers \(a,b\). Submit your answer as \(a+b\).

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