A team of engineers is designing a new type of noise-canceling headphone. The effectiveness of the noise cancellation is modeled by the polynomial $E(f) = af^3 + bf^2 + cf + d$, where $E(f)$ represents the noise reduction in decibels (dB) at a given frequency $f$ (in kHz). The engineers want the headphones to perform optimally at specific frequencies. They have determined that $E(0.5) = 0$, $E(1) = 8$, and $E(2) = 0$. Furthermore, they know that as frequency increases without bound, the effectiveness decreases, so $a < 0$.
a. Deduce the value of $d$ and justify your answer based on the context.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 2 marks, testing your understanding of Polynomial Equation Solutions. It falls under Algebra, number and structure in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers algebra of functions, inverse functions, and solutions of equations and systems of equations.
solution of polynomial equations with real coefficients of degree $n$ having up to $n$ real solutions, including numerical solutions
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