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Algebraic Methods

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Question 123

f(x)=x3−(k+2)x2+(2k+5)x−5kf(x)=x^3-(k+2)x^2+(2k+5)x-5kf(x)=x3−(k+2)x2+(2k+5)x−5k, where k k\,k is a real constant.

a.

Use the factor theorem to show that (x−k)(x - k)(x−k) is a factor of f(x)f(x)f(x).

[2]
b.

Show that f(x)=0f(x) = 0f(x)=0 only has one real root, giving your answer in terms of kkk.

[4]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.

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