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.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
