| Exam Board | SPS |
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2025 |
| Session | February |
| Topic | Roots of polynomials |
4. The cubic equation
$$2 x ^ { 3 } + 6 x ^ { 2 } - 3 x + 12 = 0$$
has roots \(\alpha , \beta\) and \(\gamma\).
Without solving the equation, find the cubic equation whose roots are ( \(\alpha + 3\) ), ( \(\beta + 3\) ) and \(( \gamma + 3 )\), giving your answer in the form \(p w ^ { 3 } + q w ^ { 2 } + r w + s = 0\), where \(p , q , r\) and \(s\) are integers to be found.
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