Quadratic Game Show

Discrete Mathematics Level 4

A contestant play a game on a game show. The contestant must place any three integers in the place of \(a,b,c\) in the following equation:


then the host will rearrange the coefficients, while wearing a blindfold. Now if the coefficients after jumbling are arranged in such a way that the quadratic cannot have any real roots, the host wins, and the contestant loses. If the host does not do it, the contestant wins. Considering the contestant has the best strategy, what is the probability that the contestant will win is given by \(\frac{x}{100}\), find \(x\). The host can jumble it as many times as he wants to.

This problem was inspired by a problem I had seen a long time ago on Brilliant. I do not remember its name, but I am not trying to plagiarise it. If someone knows the original problem, please post the link in the solution.


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