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.
306 exam-style questions on CCEA A Level Maths 1.1 Algebra and functions, covering 1.1.1 Algebra and functions, 1.1.2 Algebra and functions, 1.1.3 Algebra and functions, 1.1.4 Algebra and functions, 1.1.5 Algebra and functions, 1.1.6 Algebra and functions, 1.1.7 Algebra and functions, 1.1.8 Algebra and functions, 1.1.9 Algebra and functions, 1.1.10 Algebra and functions, 1.1.11 Algebra and functions, 1.1.12 Algebra and functions, 1.1.13 Algebra and functions, and 1.1.14 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.