How do you know when to...

Hey, I've got some AS homework and I thought I understood it all but clearly not :/ I can do the solving if the question said factorise or compete the square etc but on the sheet it just says solve and I'm not sure if I should factorise, use the quadratic formula, complete the square or put it into a graph. So is there some kind of rule that shows you the best way to solve the equation or do you just trial and error?

(edited 9 years ago)

Reply 1

_Ddraig_

19

Original post by Taelii

Hey, I've got some AS homework and I thought I understood it all but clearly not :/ I can do the solving if the question said factorise or compete the square etc but on the sheet it just says solve and I'm not sure if I should factorise, use the quadratic formula, complete the square or put it into a graph. So is there some kind of rule that shows you the best way to solve the equation or do you just trial and error?

Normally if there is no specification i normally do what ever is convenient for that particular scenario (factorising is most likely). For example;

x^2\ -\ x\ -\ 2\ =\ 0\ \longrightarrow Factorise

x^2\ +\ 6x\ +\ 1\ =\ 0\ \longrightarrow Complete\ The\ Square

x^2\ +\ x\ -\ 4\ =\ 0\ \longrightarrow Use\ Quadratic\ Formula

With practice you will soon be able to see what equations can be factorised and which can't, which equations you can complete the square for, and which equations require you to use the quadratic formula.

The only time i would disregard this, is if you have been working on a particular method in class in which the teacher has set you questions on. Sometimes worksheets can be titled with the method, then just be lazy in the questions and put 'solve' making the assumption you will use the method you have been practicing. If it is a mixed question sheet then use which ever method is appropriate.

(edited 9 years ago)

Reply 2

gdunne42

21

I assume this is about quadratics.
Unless the question states how you are required to solve the problem........
Factorise if you can, it is usually the quickest and easiest method
If it doesn't factorise then completing the square or using the formula can be used to find either exact surd solutions or solutions to a required decimal accuracy. You can also use these methods if it does factorise but you can't see how.
Plotting the curve or using trial and improvement methods should only be used if specifically stated.

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Reply 3

crashMATHS

16

Original post by Taelii

Hey, I've got some AS homework and I thought I understood it all but clearly not :/ I can do the solving if the question said factorise or compete the square etc but on the sheet it just says solve and I'm not sure if I should factorise, use the quadratic formula, complete the square or put it into a graph. So is there some kind of rule that shows you the best way to solve the equation or do you just trial and error?

You can use any of the methods. Factorising is the easiest and if it does factorise, you should use that method. If it doesn't factorise, you can use completing the square or the formula - whatever takes your fancy.

Here are some tips/hints:

1) If the question asks you to express your answer in the form

x = a \pm \sqrt b

, then complete the square, as it is easiest to use to get your answer in that form.

2) Try to see if the equation factorises firstly. To know if an equation factorises, you use this concept:

If the value of

b^2 - 4ac

is a square number, then the equation can be factorised. If not, then the equation cannot be factorised, and you have to use one of the other methods. Remember, the value of

a

and

b

are the numbers in front of

x^2

and

x

term respectively, while the value of

c

is the constant at the end of the equation.

Hope that helps.

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(edited 9 years ago)

Reply 4

waxwing

5

Original post by _Morsey_

With practice you will soon be able to see what equations can be factorised and which can't, which equations you can complete the square for, and which equations require you to use the quadratic formula.

Not to be pedantic, but you can always either complete the square or use the quadratic formula; they are the same method.

Reply 5

tombayes

12

Factorize if you can. Then quadratic formula. Sometimes if you need an answer in a particular form completing the square is necessary. But as someone said it is the same really as the quadratic formula.

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