Characterizing Cubics!

Algebra Level 5

\[\large{f(x) = x^3 + px + q}\]

Let \(f(x) = 0\) be a cubic equation such that;

  • it has one repeated root of multiplicity 2, and

  • \(p\) and \(q\) are integers such that \(q=np\) for the least permissible positive integer \(n\).

Find the value of \(p+q\).

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