Slides in this set
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
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
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
How to Work Out `x'
Using the previous example, what if it wasn't an expression
but an equation instead? - 6x² + 11x + 4 = 0
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
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