Edexcel CP AS 2022 June — Question 4

Exam BoardEdexcel
ModuleCP AS (Core Pure AS)
Year2022
SessionJune
TopicRoots of polynomials

  1. The roots of the quartic equation
$$3 x ^ { 4 } + 5 x ^ { 3 } - 7 x + 6 = 0$$ are \(\alpha , \beta , \gamma\) and \(\delta\)
Making your method clear and without solving the equation, determine the exact value of
  1. \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } + \delta ^ { 2 }\)
  2. \(\frac { 2 } { \alpha } + \frac { 2 } { \beta } + \frac { 2 } { \gamma } + \frac { 2 } { \delta }\)
  3. \(( 3 - \alpha ) ( 3 - \beta ) ( 3 - \gamma ) ( 3 - \delta )\)