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Algebraic Methods

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Question 168

Given that

f(x)=2x3−5x2+8x+k f(x) = 2x^3 - 5x^2 + 8x + k f(x)=2x3−5x2+8x+k

where kkk is a constant.

Given that (2x−1)(2x - 1)(2x−1) is a factor of f(x)f(x)f(x),

a.

use the factor theorem to show that k=−3k = -3k=−3.

[3]
b.

Hence show that the equation f(x)=0f(x) = 0f(x)=0 has only one real root.

[4]

Algebraic Methods Questions

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

Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank