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**Coursework Notes - Algebra**

**Quadratic Equations**

__Solution by factorising__ - This is best understood with an example.

solve:

You must first ask yourself which two factors when __multiplied__ will give **12 ?**

The factor pairs of **12** are : __1 x 12__, __2 x 6__ and __3 x 4__

You must decide which of these factor pairs __added or subtracted__ will give **7** ?

1 x 12 ...gives 13, 11

2 x 6 .....gives 8, 4

3 x 4 .....gives 7, 1

Which combination when multiplied makes +12 and which when added gives -7?** **

These are the choices:

(+3) (+4),
(-3) (+4),
(+3) (-4)
(-3) (-4) |

Clearly, (-3)(-4) are the two factors we want.

therefore

Now to solve the equation:

factorising, as above

either

or

for the equation to be true.

So the roots of the equation are: * *

__Completing the square __

This can be fraught with difficulty, especially if you only half understand what you are doing.

The method is to move the last term of the quadratic over to the right hand side of the equation and to add a number to both sides so that the left hand side can be factorised as the square of two terms.

e.g.

However, there is a much neater way of solving this type of problem, and that is by remembering to put the equation in the following form:

using the previous example,

__Using the Formula__ - the two solutions of quadratic equations in the form

are given by the formula:

__Example__ Find the two values of x that satisfy the following quadratic equation:

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