9231 P11 - Jun 2016 - Q1 - 4 marks
6340
The roots of the cubic equation \(2 x^{3}+x^{2}-7=0\) are \(\alpha, \beta\) and \(\gamma\). Using the substitution \(y=1+\frac{1}{x}\), or otherwise, find the cubic equation whose roots are \(1+\frac{1}{\alpha}, 1+\frac{1}{\beta}\) and \(1+\frac{1}{\gamma}\), giving your answer in the form \(a y^{3}+b y^{2}+c y+d=0\), where \(a, b, c\) and \(d\) are constants to be found.
