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1.1.10 Algebra and functions

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Question 36

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]

Markscheme

1.1.10 Algebra and functions Questions

A Level
Maths
1.1.10 Algebra and functions

64 exam-style questions on CCEA A Level Maths 1.1.10 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.

1.1.10 Algebra and functions

Question bank

1.1.10 Algebra and functions

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Question 36

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]

Markscheme

1.1.10 Algebra and functions Questions

A Level
Maths
1.1.10 Algebra and functions

64 exam-style questions on CCEA A Level Maths 1.1.10 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.