Standard +0.3 This is a standard FP1 transformation of roots question requiring a straightforward substitution (y = 3x, so x = y/3) and algebraic simplification. While it involves more algebraic manipulation than basic C1/C2 questions and is from Further Maths, the technique is routine and well-practiced, making it slightly easier than average overall difficulty.
The roots of the cubic equation \(x^3 + 3x^2 - 7x + 1 = 0\) are \(\alpha\), \(\beta\) and \(\gamma\). Find the cubic equation whose roots are \(3\alpha\), \(3\beta\) and \(3\gamma\), expressing your answer in a form with integer coefficients. [6]
The roots of the cubic equation $x^3 + 3x^2 - 7x + 1 = 0$ are $\alpha$, $\beta$ and $\gamma$. Find the cubic equation whose roots are $3\alpha$, $3\beta$ and $3\gamma$, expressing your answer in a form with integer coefficients. [6]
\hfill \mbox{\textit{OCR MEI FP1 2007 Q5 [6]}}