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.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.