Edexcel A-level Mathematics · 9MA0
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Extreme practice · Multi-step problems within A-level pure maths. Difficulty is an editorial judgement. These questions are self-reviewed, not ranked.
Calculator permitted. Show sufficient working in the spaces provided. Give inexact answers to 3 significant figures unless specified otherwise. The official exam provides a formulae and statistical tables booklet.
Original topic practice. This set is not a full official paper. Written work is self-reviewed against our worked solutions.
Let .
Show that p(x)=0 has exactly one real root α, and that .
(5)
Find a cubic equation with integer coefficients whose unique real root is 1/α. Give bounds for this root.
(4)
(Total for Question 1 is 9 marks)