An algebra problem by Archit Tripathi

Algebra Level 5

Let \(p, q, r\) be the roots of a cubic equation

\(ax^{3} + bx^{2} + cx + d = 0\).

Suppose \(a\) and \(b\) are two positive real numbers such that the roots of the cubic equation \(x^{3} - ax + b = 0\) are all real.

Let \(p\) is a root of this cubic equation with minimal absolute value. The range of values of \(p\) is given by \(\text{_________}.\)

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