9231 P11 - Jun 2011 - Q2 - 6 marks
6477
The roots of the equation
\(x^{3}+p x^{2}+q x+r=0\)
are \(\frac{\beta}{k}, \beta, k \beta\), where \(p, q, r, k\) and \(\beta\) are non-zero real constants. Show that \(\beta=-\frac{q}{p}\).
Deduce that \(r p^{3}=q^{3}\).
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