SPS SPS FM Pure 2025 February — Question 4

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2025
SessionFebruary
TopicRoots 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.
[0pt] [BLANK PAGE]