Edexcel F1 2021 January — Question 4

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2021
SessionJanuary
TopicRoots of polynomials

  1. The equation \(2 x ^ { 2 } + 5 x + 7 = 0\) has roots \(\alpha\) and \(\beta\)
Without solving the equation
  1. determine the exact value of \(\alpha ^ { 3 } + \beta ^ { 3 }\)
  2. form a quadratic equation, with integer coefficients, which has roots $$\frac { \alpha ^ { 2 } } { \beta } \text { and } \frac { \beta ^ { 2 } } { \alpha }$$ \includegraphics[max width=\textwidth, alt={}, center]{f8660b02-384e-460f-a0e4-282ef5fef475-09_2255_50_314_34}
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