Use the quadratic formula to solve an equation in terms of an unknown variable

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Transition to university :

Christian Lawson-Perfect	said	Ready to use	7 years, 8 months ago
Hannah Aldous	said	Needs to be tested	7 years, 9 months ago
Chris Graham	said	Has some problems	7 years, 9 months ago
Vicky Hall	said	Has some problems	7 years, 9 months ago

History

○

Elliott Fletcher 7 years, 8 months ago

Published this.

○

Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

Looks good!

Restore this checkpoint

○

Hannah Aldous 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Christian Lawson-Perfect 7 years, 9 months ago

Gave some feedback: Has some problems

○

Christian Lawson-Perfect 7 years, 9 months ago

Saved a checkpoint:

The marking is set up wrong: $k(-6)$ is the application of the function $k$ , not $-6 \times k$ . You can avoid this by writing $(\ldots)k$ instead of $k(\ldots)$ .

It's not obvious what order you should enter the roots. The best I can come up with for a hint is "Assuming $k$ is positive, enter the lowest root first." I can't think how to be any clearer without giving a hint about the form of the answer.

You need \left and \right around brackets to make sure they stretch to fit around fractions.

Put the quadratic formula in the advice just before you list the values for $a$ , $b$ and $c$ .

Restore this checkpoint

○

Chris Graham 7 years, 9 months ago

Gave some feedback: Has some problems

○

Chris Graham commented 7 years, 9 months ago

When the variable C_2 is zero, your advice states $c = 0k^2$ , which caused me great confusion (about where the $k^2$ had come from) when I was unlucky enough to generate this on my first attempt. If you would like to keep this scenario, then you will need to adjust the advice, or if it is not desirable then use an except in the generation of B_2 or n2.

○

Hannah Aldous 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Vicky Hall 7 years, 9 months ago

Gave some feedback: Has some problems

○

Vicky Hall commented 7 years, 9 months ago

This is a well conceived question but the answers look a bit nasty! It would be a much nicer question if, when we get to the point of having $\sqrt(xk^2)$ , the $x$ is a square number. That way we end up with some quantity of $k$ divided by $2$ , which may or may not simplify, but it looks a lot better than having a surd or a decimal.

○

Hannah Aldous 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Hannah Aldous 7 years, 9 months ago

Created this as a copy of Using the Quadratic Formula to Solve Equations of the Form

$ax^2 +bx+c=0$ .

Name	Status	Author	Last Modified
Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$	Ready to use	Hannah Aldous	07/01/2021 14:29
Use the quadratic formula to solve an equation in terms of an unknown variable	Ready to use	Hannah Aldous	20/11/2019 14:44
Katherine's copy of Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$	draft	Katherine Tomlinson	02/08/2017 12:45
Emma's copy of Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$	draft	Emma Cliffe	31/08/2017 12:59
Peter's copy of Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$	draft	Peter Knowles	12/09/2017 12:39
Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$ [L4 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 11:06
Simon's copy of Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$	draft	Simon Thomas	07/03/2019 09:55
Simon's copy of Use the quadratic formula to solve an equation in terms of an unknown variable	draft	Simon Thomas	07/03/2019 10:00
Use the quadratic formula to solve an equation in terms of an unknown variable	draft	Xiaodan Leng	11/07/2019 01:50
Solve Equations of the Form $ax^2 +bx+c=0$	draft	Thomas Waters	11/09/2019 22:18
Ugur's copy of Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$	Ready to use	Ugur Efem	08/11/2021 16:44
Ugur's copy of Ugur's copy of Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$	Ready to use	Ugur Efem	28/04/2022 11:08

There are 59 other versions that do you not have access to.

Question statement

The coefficients of the following equation involve the unknown value $k$ . We can use the quadratic formula to find expressions for the values of $x$ in terms of $k$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

b	number	7
c	number	9
n2	number	16
b_2	number	36
c_2	number	5
b_3	number	6

			Name	Type	Generated Value

a1	integer	1
a2	integer	9
a3	integer	-3
a4	integer	13
b1	integer	6
b2	integer	27
b3	integer	-20
b4	integer	5
x1	number	-10.5207972894
p1	number	-4.4206957827
p2	number	0.754029116
x2	number	1.5207972894
a	integer	18
m	integer	12

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
2c^0.5+a1^2

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Mathematical expression
  Add
1. Step Information only

Gap-fill

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

Solve the equation $\simplify {x^2+{b_3}*k*x+{c_2}k^2=0}$ . Give your answer in terms of $k$ . Assuming $k$ is positive, enter the lowest root first.

$x_1=$ Gap 0.

$x_2=$ Gap 1.

Advice

The quadratic formula is

${\frac {-b\pm\sqrt{b^2-4\times a\times c}}{2a}}\text{.}$

We can list our values for $a, b$ and $c$ .

$\begin{align} a&=1\\ b&=\var{b_3}k\\ c&=\var{c_2}k^2 \end{align}$

Then by substituting them into the quadratic formula, we obtain

$x=\frac {-\var{b_3}k\pm\sqrt{\var{b_3}^2k^2-4\times \var{c_2}k^2}}{2}$

We can then simplify this equation to

$\begin{align} x&=\frac {-\var{b_3}k\pm k\sqrt{\var{b_3}^2-\var{4c_2}}}{2}\\ \end{align}$

$\begin{align} &=k\left(\frac{-\var{b_3}}{2}\pm \frac {\sqrt{\var{b_3}^2-\var{4c_2}}}{2}\right)\\ \end{align}$

$\begin{align} &=k\left(-\frac{\var{b_3}}{2} \pm\frac{\sqrt{\var{(b_3^2-4c_2)}}}{2}\right)\\ \end{align}$

This means our possible values for $x$ in terms of $k$ are,

$\begin{align} x_1 &= \left( \simplify[all,!noleadingminus,!collectnumbers,!simplifyfractions]{-{b_3}/2 - {sqrt(b_3^2-4c_2)}/2} \right) k = \var[fractionnumbers]{-b_3/2 - sqrt(b_3^2-4*c_2)/2}k \\ x_2 &= \left( \simplify[all,!noleadingminus,!collectnumbers,!simplifyfractions]{-{b_3}/2 + {sqrt(b_3^2-4c_2)}/2} \right) k = \var[fractionnumbers]{-b_3/2 + sqrt(b_3^2-4*c_2)/2}k \end{align}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Information only

This question is used in the following exams:

Summer Project (Optimisation + Methods of proof) by Inbbavathie Ravi in Inbbavathie's workspace.
summer project 2 ( egyptian fractions+complex numbers) by Inbbavathie Ravi in Inbbavathie's workspace.
summer project 3 (modular arithmetic + induction) by George Loughlin in George's workspace.
Quadratic expressions and equations by Christian Lawson-Perfect in Transition to university.
Nick's copy of Quadratic expressions and equations by Nick Walker in Nick's workspace.
Quadratic expressions and equations [Randomised L4] by Matthew James Sykes in CHY1205.
NUMBAS - Quadratics by Katy Dobson in Katy's workspace.
Ann's copy of NUMBAS - Quadratics by Ann Smith in Ann's workspace.
Summer Project 2 - practice by Inbbavathie Ravi in NCL MSP International Summer Project.
Summer Project 3 - practice by Inbbavathie Ravi in NCL MSP International Summer Project.
Blathnaid's copy of Ann's copy of NUMBAS - Quadratics by Blathnaid Sheridan in Blathnaid's workspace.
MATH1601 Quiz 3 by Blathnaid Sheridan in Blathnaid's workspace.
Quadratics by Kevin Bohan in Kevin's workspace.
lksadjf by Jordan Childs in Jordan's workspace.
Workbook 7 by Jordan Childs in Jordan's workspace.
Workbook 6 by Jordan Childs in Jordan's workspace.
MATH1601 CA1 Semester 1 by Blathnaid Sheridan in Blathnaid's workspace.
PH022 Week 4 Quadratics Quiz by Vicky Mason in Vicky's workspace.
QuadraticEquationAndExpression by AJAY OTTA in AJAY's workspace.
Algebra by Alan Levine in Mathtest Questions.
test exam algebra by Jose Camarena Brenes in Jose's workspace.
Quadratic expressions and equations by Wan Mekwi in Introduction to Calculus.
Using the Quadratic Formula to Solve Equations of the Form ax2+bx+c=0 by Ahmed Al-Razaz in Resources.
Jean jinhua's copy of Quadratic expressions and equations by Jinhua Mathias in Jinhua's workspace.
Solving Quadratics by Kevin Bohan in Kevin's workspace.
Edina's copy of Quadratic expressions and equations by Edina Kurdi in Edina's workspace.
Module 3 by Niharika Singh in Niharika's workspace.
Week 1 revision by Sara Santos in Sara's workspace.
first exam by Sara Santos in Sara's workspace.
Assignment 5 - Algebra | Part 2 by Ahmed Al-Razaz in IA128-Ahmed.
Quiz1 by Matt Falk in Matt's workspace.
Quadratic expressions and equations by AJAY OTTA in Aaron.
claire's copy of Quadratic expressions and equations by claire lines in claire's workspace.
Algebra II by Chris Templet in Chris's workspace.
ME0006 Wk 1 Test 2 by claire lines in claire's workspace.
Excellent quadratic equations questions and answers by Nahid Chowdhury in FS0031 Unit 3.
Q by Dean Ang in Dean's workspace.

Loading...

Error

Use the quadratic formula to solve an equation in terms of an unknown variable

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Hannah Aldous 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Hannah Aldous 7 years, 9 months ago

Vicky Hall 7 years, 9 months ago

Vicky Hall commented 7 years, 9 months ago

Hannah Aldous 7 years, 9 months ago

Hannah Aldous 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Use the quadratic formula to solve an equation in terms of an unknown variable

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Hannah Aldous 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Hannah Aldous 7 years, 9 months ago

Vicky Hall 7 years, 9 months ago

Vicky Hall commented 7 years, 9 months ago

Hannah Aldous 7 years, 9 months ago

Hannah Aldous 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`