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Slide 1

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Solving Quadratic Equations
It is alright if you have no clue about how to work out
quadratic equations. This section will teach you one of
the simplest ways to work it out.
Good Luck!!…read more

Slide 2

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What?
Quadratic equations are in the form: ax² + bx + c
The question will ask you to work out x or simplify the
equation. Just remember these two important points:
Expression: ax² + bx + c - the equation does not equal
a value so x cannot be solved for.
Equation: ax² + bx + c = y - the equation does equal a
value and so x can be solved for.…read more

Slide 3

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How to Simplify the Expression
Simplify the following expression:
6x² + 11 x + 4
You take the expression and look at the first and last
integers to start of with: 6 and 4
You multiply the two numbers: 6 x 4 = 24
Now, you find two factors of 24 that add to make 11
24 = 3 x 8 ... 3 + 8 = 11
You substitute the 11 in exchange for the 3 and 8
Note: it makes no difference in which order the numbers
are substituted…read more

Slide 4

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How to Simplify Cont...
You should now be left with the equation:
6x² + 3x + 8x + 4
You now split the expression down the middle:
6x² + 3x + 8x + 4
Factorise both halves...
3x (2x + 1) + 4 (2x + 1) - The expression inside both
brackets MUST BE THE SAME!!!
You have now got two brackets: (3x + 4)(2x + 1)
You have simplified the expression.…read more

Slide 5

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How to Work Out `x'
Using the previous example, what if it wasn't an expression
but an equation instead? - 6x² + 11x + 4 = 0
Simple...
Repeat the previous steps until your left with:
(3x + 4)(2x + 1) = 0
Now you must assume that both brackets equal 0...
3x + 4 = 0 | 2x + 1 = 0
Work out x:
3x = -4 | 2x = -1
x = -4/3 or x = -½
You MUST NOT forget the `or' else you will lose a mark!…read more

Slide 6

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What if?
What if the equation was: 4x² - 4x ­ 3 = 0
You still multiply the two digits but remember it is -3:
4 x -3 = -12
Find the factors that add to make 4: -6 + 2
And carry on the method...
4x² - 6x + 2x ­ 3 = 0
2x (2x ­ 3) + 1 (2x ­ 3) = 0
(2x + 1)(2x ­ 3) = 0
x = -½ or x = 3/2…read more

Slide 7

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