1.3.1 Operations on polynomials

The internal pressure $P\,$ of a experimental gas chamber is modeled by the function:

P(v) = 3v^3 + 13v^2 + 19v + k

where $v\,$ is the relative volume and $k\,$ is a constant.

Given that $(3 v + 1)$ is a factor of $P (v)$ ,

use the factor theorem to show that $k = 5$ .

[2]

Hence show that the equation $P (v) = 0$ has only one real root.

[4]

1.3.1 Operations on polynomials Questions

The internal pressure $P\,$ of a experimental gas chamber is modeled by the function:

P(v) = 3v^3 + 13v^2 + 19v + k

where $v\,$ is the relative volume and $k\,$ is a constant.

Given that $(3 v + 1)$ is a factor of $P (v)$ ,

use the factor theorem to show that $k = 5$ .

[2]

Hence show that the equation $P (v) = 0$ has only one real root.

[4]