Solving quadratic equations 1(c)

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Frank Doheny

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Frank Doheny

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7 years, 4 months ago

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Frank Doheny 7 years, 4 months ago

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Frank Doheny 8 years, 4 months ago

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Frank Doheny 8 years, 6 months ago

Created this as a copy of Solving quadratic equations 1(a).

Name	Status	Author	Last Modified
Solving quadratic equations 1(a)	Ready to use	Frank Doheny	24/11/2017 07:43
Solving quadratic equations 1(c)	Ready to use	Frank Doheny	24/11/2017 07:51
Solving quadratic equations 1(b)	Ready to use	Frank Doheny	24/11/2017 07:36
Solving quadratic equations	draft	Nigel Atkins	02/03/2017 08:53
David's copy of Solving quadratic equations	draft	David Wishart	06/04/2017 18:38
Andrew's copy of Solving quadratic equations 1(b)	draft	Andrew Dunbar	30/06/2017 22:04
ecuacion cuadratica 1	draft	Ricardo Monge	04/10/2017 14:18
ecuacion cuadratica 2	draft	Ricardo Monge	04/10/2017 14:17
ecuacion cuadratica 3	draft	Ricardo Monge	04/10/2017 14:19
Maria's copy of Solving quadratic equations 1(b)	draft	Maria Aneiros	29/05/2019 07:18
Ugur's copy of Solving quadratic equations 1(a)	Ready to use	Ugur Efem	04/11/2021 15:33

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Question statement

The following equation can be converted into a quadratic equation:

$\var{a1}x+\frac{\simplify{{a1}*{b1}*{c1}}}{x}=\simplify{{a1}*({b1}+{c1})}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	4
b1	integer	21
c1	integer	7
b	integer	112
c	integer	588

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Generated value: `integer`

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2. Gap Gap 1. Number entry
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Type in the greater of the two values that satisfies the equation.

$x =$ Gap 0.

Type in the lesser of the two values that satisfies the equation.

$x =$ Gap 1.

Advice

$\var{a1}x+\frac{\simplify{{a1}*{b1}*{c1}}}{x}=\simplify{{a1}*({b1}+{c1})}$

We clear the fraction in the equation by multiplying across by $x$

$\var{a1}x^2+\simplify{{a1}*{b1}*{c1}}=\simplify{{a1}*({b1}+{c1})}x$

Bringing all the terms to the left hand side and putting them in order of their powers of $x$ gives

$\var{a1}x^2-\simplify{{a1}*({b1}+{c1})}x+\simplify{{a1}*{b1}*{c1}}=0$

The formula for solving a quadratic equation of the form $ax^2+bx+c=0$ is given by

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

In this example $a=\var{a1},\,\,\,b=\simplify{+-{a1}*({b1}+{c1})}$ and $c=\simplify{{a1}*{b1}*{c1}}$

$x=\frac{\var{b}\pm \sqrt{(-\var{b})^2-4*\var{a1}*\var{c}}}{2*\var{a1}}$

$x=\frac{\var{b}\pm \sqrt{\simplify{{b}^2-4*{a1}*{c}}}}{\simplify{2*{a1}}}$

$x=\simplify{{b}+({b}^2-4*{a1}*{c})^0.5}/\simplify{2*{a1}}=\simplify{({b}+({b}^2-4*{a1}*{c})^0.5)/(2*{a1})}$ or $x=\simplify{{b}-({b}^2-4*{a1}*{c})^0.5}/\simplify{2*{a1}}=\simplify{({b}-({b}^2-4*{a1}*{c})^0.5)/(2*{a1})}$

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Frank Doheny 7 years, 4 months ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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Solving quadratic equations 1(c)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 7 years, 4 months ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`