Quadratics: Interpreting the Discriminant

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Ben McGovern

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3 years, 8 months ago

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Ben McGovern 2 years, 6 months ago

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Ben McGovern 3 years, 8 months ago

Gave some feedback: Ready to use

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Ben McGovern 4 years, 9 months ago

Created this as a copy of Quadratics: Completing the Square 2.

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

By evaluating the discriminant, determine how many roots the following quadratic equation has:

$\simplify[all]{{a}x^2+{b}x+{c}}=0.$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
b	integer	2
c	integer	-2
eval	string	<p>So for $\simplify[all]{{a}x
eval2	string	<p>So for $\simplify[all]{{a}x
roots1	string	<p>So for $\simplify[all]{{a}x
roots2	string	<p>So for $\simplify[all]{{a}x
rootsNo	string	<p>So for $\simplify[all]{{a}x
sol	integer	2

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Generated value: `integer`

→ Used by:

eval
eval2
roots1
roots2
rootsNo
sol

Statement
Advice

Parts

Gap-fill
1. Gap Mathematical expression
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Number of roots: Unnamed gap

Advice

For a quadratic expression equation of the form \[ ax^2+bx+c = 0,\] the discriminant is \[ b^2-4ac.\]

If $b^2-4ac > 0$, the equation has 2 distinct real roots;
If $b^2-4ac = 0$, the equation has 1 distinct real root;
If $b^2-4ac < 0$, the equation has no real roots.

{eval}

{geogebra_applet('https://www.geogebra.org/m/md6w6cs9',[a: a, b: b, c: c])}

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This question is used in the following exams:

Quadratic Functions Quiz by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Quadratics by Ben McGovern in MASH Bath: Moodle quizzes and TS.
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.
Class Test 1 23/24 by Ruth Douglas in Ruth's workspace.
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.

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Ben McGovern 2 years, 6 months ago

Ben McGovern 3 years, 8 months ago

Ben McGovern 4 years, 9 months ago

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Generated value: `integer`

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Quadratics: Interpreting the Discriminant

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 2 years, 6 months ago

Ben McGovern 3 years, 8 months ago

Ben McGovern 4 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`