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.
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.