Simple irreducible quadratic factor partial fractions

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Frank Doheny

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Frank Doheny 7 years, 5 months ago

Created this as a copy of Repeated linear factor partial fractions.

Name	Status	Author	Last Modified
Manipulation of formula 2	Ready to use	Frank Doheny	24/11/2017 08:16
simple linear factors partial fractions	draft	Frank Doheny	27/09/2022 21:18
Repeated linear factor partial fractions	draft	Frank Doheny	24/10/2017 16:58
Despeje de variable	draft	Ricardo Monge	03/10/2017 22:02
Simple irreducible quadratic factor partial fractions	draft	Frank Doheny	24/10/2017 16:58
Irreducible quadratic factor partial fractions	draft	Frank Doheny	13/11/2017 08:17
Irreducible quadratic factor partial fractions	draft	Frank Doheny	28/11/2017 18:12
Maria's copy of Manipulation of formula 2	draft	Maria Aneiros	25/05/2019 07:25

There are 12 other versions that do you not have access to.

Question statement

Determine the partial fraction breakdown of the following expression:

$I(s)=\frac{\var{R}s^2+\var{T}}{(s+\var{a})(s^2+\simplify{{b}^2})}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	1
b	integer	5
T	integer	11
R	integer	4

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A random number between and (inclusive) with step size

Description

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Generated value: `integer`

→ Used by:

Statement
"Unnamed part" → "Unnamed gap" - Correct answer

Parts

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1. Gap Mathematical expression
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Express your answer as a sum fractions:

$I(s) =$ Unnamed gap

Advice

$\frac{\var{R}s^2+\var{T}}{(s+\var{a})(s^2+\simplify{{b}^2})}=\frac{A}{s+\var{a}}+\frac{Bs+C}{(s^2+\simplify{{b}^2})}$

Mutiply across by the denominator $(s+\var{a})(s^2+\simplify{{b}^2})$ to get

$\var{R}s^2+\var{T}=A(s^2+\simplify{{b}^2})+Bs(s+\var{a})+C(s+\var{a})$

let s = $-\var{a}$

$\simplify{{R}*{a}^2+{T}}=\simplify{({a}^2+{b}^2)}A$

$A=\simplify{({R}*{a}^2+{T})/({a}^2+{b}^2)}$

let s = $0$

$\var{T}=\simplify{{b}^2}A+\var{a}C$

$\var{T}-\simplify{{b}^2}*\simplify{{({R}*{a}^2+{T})/({a}^2+{b}^2)}=\var{a}C$

$C=\simplify{({a}*{T}-{a}*{R}*{b}^2)/({a^2}+{b}^2)}$

coefficient of $s^2 = \var{R}$

$\var{R}=A+B$

$B=\var{R}-A$

$B=\simplify{({R}*{b}^2-{T})/({a}^2+{b}^2)}$

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This question is used in the following exam:

Year 2 Laplace: Continuous Assessment quiz by Frank Doheny in Laplace transforms & Differential equations for computer engineering.

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Simple irreducible quadratic factor partial fractions

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Frank Doheny 7 years, 5 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

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Gap-fill

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Error

Simple irreducible quadratic factor partial fractions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Frank Doheny 7 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`