The displacement of a particle $s$ (in meters) from a reference point at time $t$ (in seconds) is modeled by the function:

s(t) = (t - 2)(3t^2 + 10t + k) + 48

where $k\,$ is a constant.

State the remainder when $s (t)$ is divided by $(t - 2)$ .

Given that the particle is at the reference point ( $s = 0$ ) when $t=23\displaystyle t = \frac{2}{3}$ , show that $k = 28$ .

Hence

fully factorise the expression for $s (t)$ ,

Hence

find the number of real solutions of the equation $s (t) = 0$ , giving a reason for your answer.

The displacement of a particle $s$ (in meters) from a reference point at time $t$ (in seconds) is modeled by the function:

s(t) = (t - 2)(3t^2 + 10t + k) + 48

where $k\,$ is a constant.

State the remainder when $s (t)$ is divided by $(t - 2)$ .

Given that the particle is at the reference point ( $s = 0$ ) when $t=23\displaystyle t = \frac{2}{3}$ , show that $k = 28$ .

Hence

fully factorise the expression for $s (t)$ ,

Hence

find the number of real solutions of the equation $s (t) = 0$ , giving a reason for your answer.

1.1 Algebra and functions

1.1 Algebra and functions Questions