Given that
f(x)=2x3−5x2+8x+k f(x) = 2x^3 - 5x^2 + 8x + k f(x)=2x3−5x2+8x+kwhere 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.
181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.