Quelpr
4 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2007 · Paper 2 · Question 2(b)(ii)

The quadratic equation x^2 - px + 24 = 0, p ∈ R, has roots α and β, and the quadratic equation x^2 - 8x + q = 0, q ∈ R, has roots 2α + β and 2α - β.

Find the values of α and β.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 2(a)Find the value of n for which 3S_{2n} = 11 S_n. Note: Σr = n(n+1)/2.[4 marks]
  2. 2(b)(i)Express p and q in terms of α and β.[2 marks]
  3. 2(b)(iii)Hence, determine the values of p and q.[2 marks]
  4. 2(c)Prove, by Mathematical Induction, that n^2 > 2n for all integers n ≥ 3.[8 marks]

More practice: the rest of this paper · more Algebraic Operations questions · all CAPE Pure Mathematics Unit 1 past papers