Given that f(x)=2x3−5x2+8x+kf(x) = 2x^3 - 5x^2 + 8x + kf(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),
use the factor theorem to show that k=−3k = -3k=−3.
Hence show that the equation f(x)=0f(x) = 0f(x)=0 has only one real root.
Practise Edexcel A Level Maths 1.5 Algebraic Division with exam-style questions for A Level Maths. 65 questions, 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.