Quadratics: Solving by Factorisation

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2 years, 6 months ago

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Ben McGovern 2 years, 6 months ago

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Ben McGovern 2 years, 6 months ago

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Ben McGovern 3 years, 6 months ago

Created this as a copy of Quadratics: Factorisation 1.

Name	Status	Author	Last Modified
Surds: Simplifying Expressions 1a	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 1b	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 2b	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 2a	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 3a	Ready to use	Ben McGovern	15/08/2023 15:31
Surds: Simplifying Expressions 3b	Ready to use	Ben McGovern	15/08/2023 15:14
Surds: Simplifying Expressions 4a	Ready to use	Ben McGovern	15/08/2023 15:29
Surds: Simplifying Expressions 4b	Ready to use	Ben McGovern	15/08/2023 15:26
Surds: Simplifying Expressions 4c	Ready to use	Ben McGovern	15/08/2023 15:50
Surds: Simplifying Expressions 5a - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 15:55
Surds: Simplifying Expressions 5b - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 16:07
Surds: Simplifying Expressions 6 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Surds: Simplifying Expressions 7 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Quadratics: Using the Quadratic Formula	Ready to use	Ben McGovern	14/09/2022 16:14
Quadratics: Factorisation 1	Ready to use	Ben McGovern	14/08/2023 15:01
Quadratics: Factorisation 2	Ready to use	Ben McGovern	14/08/2023 15:14
Quadratics: Completing the Square 1	Ready to use	Ben McGovern	14/08/2023 14:59
Quadratics: Completing the Square 2	Ready to use	Ben McGovern	14/09/2022 16:03
Quadratics: Interpreting the Discriminant	Ready to use	Ben McGovern	14/09/2022 16:08
Quadratics: Factorisation 3 - Difference of 2 squares	Ready to use	Ben McGovern	14/08/2023 15:33
Indices: Simplification 1a	Ready to use	Ben McGovern	26/06/2023 12:12
Indices: Simplification 1b	Ready to use	Ben McGovern	26/06/2023 14:31
Indices: Simplification 1c	Ready to use	Ben McGovern	26/06/2023 14:30
Indices: Simplification 2a	Ready to use	Ben McGovern	26/06/2023 14:33
Indices: Simplification 2b	Ready to use	Ben McGovern	26/06/2023 14:36
Indices: Simplification 3a	Ready to use	Ben McGovern	26/06/2023 14:37
Indices: Simplification 3b	Ready to use	Ben McGovern	26/06/2023 14:40
Indices: Change of Notation 1	Ready to use	Ben McGovern	15/08/2023 11:43
Indices: Change of Notation 2	Ready to use	Ben McGovern	15/08/2023 11:51
Indices: Change of Notation 3	Ready to use	Ben McGovern	15/08/2023 11:54
Solve Quadratics - Factorisation 1	Ready to use	Ruth Hand	14/08/2023 15:44
Quadratics: Solving a Quadratic Equation	Ready to use	Ben McGovern	09/12/2022 16:45
Quadratics: Solving by Factorisation	Ready to use	Ben McGovern	14/09/2022 16:25
AD2 Quadratics - solve	Ready to use	Megan Oliver	09/04/2024 15:13
AD5 Difference of two squares	Ready to use	Megan Oliver	09/04/2024 15:14
AA2 Indices - divide	Ready to use	Andrew Neate	09/04/2024 15:00
AA4 Indices - Fractional 2	Ready to use	Andrew Neate	09/04/2024 15:01
AA3 Indices - Fractional 1	Ready to use	Andrew Neate	09/04/2024 15:01
AA1 Indices - times	Ready to use	Andrew Neate	28/03/2024 13:17
Calculation with indices - times	Ready to use	Will Morgan	26/06/2024 11:53
Calculation with Indices - divide	Ready to use	Will Morgan	26/06/2024 12:07

There are 209 other versions that do you not have access to.

Question statement

Solve the following quadratic equation by factorisation or otherwise:

$\simplify[unitFactor]{x^2+{b}x+{c}=0}$

Give any introductory information the student needs.

			Name	Type	Generated Value

b	integer	16
c	integer	60
p	integer	10
q	integer	6
sol	list	[ -10, -6 ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
{p+q}

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Description

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Generated value: `integer`

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1. Gap List of numbers
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Advice

To solve a quadratic equation of the form

$x^2+bx+c=0$ by factorisation, we want to factorise the equation into the form

$(x+p)(x+q)=0,$ where

$p+q=b$ and

$p \times q = c$ .

Hence, for the equation

$\simplify{x^2+{b}x+{c}=0},$

this can be factorised to

$\simplify{(x+{p})(x+{q})=0}.$ This equation is satisfied when either

$\simplify{x+{p}=0} \quad \text{or} \quad \simplify{x+{q}=0},$ which implies the solutions to this quadratic equation are

$\simplify{x={-p}} \quad \text{and} \quad \simplify{x={-q}} .$

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This question is used in the following exams:

Quadratics practice by Ruth Douglas in Ruth's workspace.
All about quadratics by Jinhua Mathias in Maths 3-2020.
Maths 1A Week 2 Online Homework by Maria Aneiros in Maria's workspace.
All the good stuff by Chris Templet in Chris's workspace.
test_bots3_vs_bots5 by Raul Duarte in themes.
Algebra - MASH questions by Morgiane Richard in Mathematics for Geosciences.
Subject Knowledge Homework 1 by Ciaran Cassidy in A Level Subject Knowledge Homework.
Mixed practice on quadratic equations by Jinhua Mathias in Maths 3-2020.
Summer Quiz 1 by Kate Vincent in Kate's workspace.

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Ben McGovern 2 years, 6 months ago

Ben McGovern 2 years, 6 months ago

Ben McGovern 3 years, 6 months ago

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Generated value: `integer`

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Quadratics: Solving by Factorisation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 2 years, 6 months ago

Ben McGovern 2 years, 6 months ago

Ben McGovern 3 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`