The displacement of a particle sss (in meters) from a reference point at time ttt (in seconds) is modeled by the function:
s(t)=(t−2)(3t2+10t+k)+48 s(t) = (t - 2)(3t^2 + 10t + k) + 48 s(t)=(t−2)(3t2+10t+k)+48where k k\,k is a constant.
State the remainder when s(t)s(t)s(t) is divided by (t−2)(t - 2)(t−2).
Given that the particle is at the reference point (s=0s = 0s=0) when t=23\displaystyle t = \frac{2}{3}t=32, show that k=28k = 28k=28.
Hence
fully factorise the expression for s(t)s(t)s(t),
Hence
find the number of real solutions of the equation s(t)=0s(t) = 0s(t)=0, giving a reason for your answer.
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.
