9231 P11 - Nov 2018 - Q2 - 6 marks
5871
The roots of the equation
\(x^{3}+p x^{2}+q x+r=0\)
are \(\alpha, 2 \alpha, 4 \alpha\), where \(p, q, r\) and \(\alpha\) are non-zero real constants.
(i) Show that
\(2 p \alpha+q=0 .\)
(ii) Show that
\(p^{3} r-q^{3}=0 .\)
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