| Exam Board | Edexcel |
|---|---|
| Module | CP AS (Core Pure AS) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Substitution to find new equation |
| Difficulty | Standard +0.2 Standard substitution method: let w = x-1, so x = w+1, then substitute into the cubic and expand. This is a routine Further Maths technique with straightforward algebra, typical of specimen/introductory questions. |
\begin{enumerate}
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\item The cubic equation
\end{enumerate}
$$x ^ { 3 } + 3 x ^ { 2 } - 8 x + 6 = 0$$
has roots $\alpha , \beta$ and $\gamma$.\\
Without solving the equation, find the cubic equation whose roots are $( \alpha - 1 ) , ( \beta - 1 )$ and $( \gamma - 1 )$, giving your answer in the form $w ^ { 3 } + p w ^ { 2 } + q w + r = 0$, where $p , q$ and $r$ are integers to be found.\\
(5)
\hfill \mbox{\textit{Edexcel CP AS Q4 [5]}}