Stationary Points

Calculus Level 3

Consider the polynomial function \(f\left( x \right)\) with rule \(f\left( x \right) =\frac { 1 }{ 3 } { x }^{ 3 }+a{ x }^{ 2 }-2x-2\), where \(a\in \Re. \)

What is the probability that the stationary points of \(f\left( x \right)\) lie in the same quadrant of the cartesian plane?

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