# 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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