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Papers 1 and 2 · Pure9.2 Numerical methods

Question 1 · 8 marks

  • Calculator allowed
Spec and skills
  • Paper scope: Pure 1/2
  • Spec P9.2
  • Original practice question
f(x)=x3−5x+1f(x) = x^3 - 5x + 1. The equation f(x)=0f(x) = 0 has a root α\alpha between 2 and 2.2.
(a)
Show that f(x)=0f(x) = 0 can be rearranged to x=5−1xx = \sqrt{5 - \frac{1}{x}}, for x>0x > 0.
2 marks

Divide x3−5x+1=0x^3 - 5x + 1 = 0 by x≠0x \neq 0.

Start with the key line of working.