Factorising quadratics - (easy) Example 1
Factorise the quadratic `x^2+7x+10`
Therefore the factors of 10 are:
1 and 10
2 and 5
Now ask yourself what factors of `c` add to give `b`.
i.e. what factors of 10 equal 7.
Can be written as:
Check by multiplying out:
The shock is that `(x+2)(x+5)` also gives you the roots of `x^2+7x+10=0`
Separate the brackets and put them equal to zero.
Now solve for `x`
Therefore `x=-2` and `x=-5`
The roots of `x^2+7x+10=0` are `x=-2` and `x=-5`
This example has also been used in completing the square examples and quadratic formula examples to show that the roots `-2` and `-5` can be found using any of these methods.