Solve quadratic equations by factorising
Quadratic equations have the general form:
ax^{2} + bx + c = 0
When factorising a quadratic they are usually into a pair of brackets.
For example: x^{2 }+ 5x + 6 = 0 (x + 2)(x + 3) = 0
This is useful, because once they are factorised, we can solve them easily (i.e. find out what x must be).
We have two numbers (each of the two brackets) which when multiplied together, make 0. You can make 0 by at least one of the brackets being zero (since any number multiplied by zero is zero! e.g. 2 x 0 = 0, 56 x 0 = 0, 0 x 3 x 320 = 0. )
So, whatever x is, each bracket must add up to 0 for the result to = 0.
For the first bracket, x must be 2, since (2 + 2)(2 + 3) = 0 x 1 = 0.
For the second bracket, x must be 3, since (3 + 2)(3 + 3) = 1 x 0 = 0.
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