A mechanical engineer determines that the stability factor, SSS, of a dampening system is modeled by the function S(ω)=6ω3−5ω2−17ω+6S(\omega) = 6\omega^3 - 5\omega^2 - 17\omega + 6S(ω)=6ω3−5ω2−17ω+6, where ω\omegaω is a frequency parameter.
Use the factor theorem to show that (3ω−1)(3\omega - 1)(3ω−1) is a factor of S(ω)S(\omega)S(ω).
Hence, using algebraic methods, express S(ω)S(\omega)S(ω) as the product of three linear factors.
Solve, for 0<ϕ<π0 < \phi < \pi0<ϕ<π, the equation
6tan3ϕ−5tan2ϕ−17tanϕ+6=0 6\tan^3 \phi - 5\tan^2 \phi - 17\tan \phi + 6 = 0 6tan3ϕ−5tan2ϕ−17tanϕ+6=0giving your answers to 3 significant figures.
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.