SPS SPS FM Pure 2020 February — Question 5

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2020
SessionFebruary
TopicRoots of polynomials

5 The roots of the equation \(\quad 3 x ^ { 3 } + 2 x ^ { 2 } - 7 x - 6 = 0\) are \(\alpha , \beta\) and \(\gamma\).
  1. Find the value of \(\alpha \beta \gamma\).
  2. Hence, by making use of a suitable substitution, or otherwise, find a cubic equation whose roots are \(\alpha \left( 1 + \frac { 1 } { \alpha \beta \gamma } \right) , \beta \left( 1 + \frac { 1 } { \alpha \beta \gamma } \right) , \gamma \left( 1 + \frac { 1 } { \alpha \beta \gamma } \right)\).