How do i solve the quadratic x^2 + 5x + 6 = 0 ?

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So we can always substitute the right terms into the quadratic formula. However, there might be a quicker way. Lets try and see if the quicker ways work.

Firstly, we need to spot weather the difference of two squares applies to this equation. However, as there are three terms in the equation, this cannot be the case. Difference of two squares is when the solution to x^2 - 25 is (x + 5)(x - 5). 

Then we can try and find two numbers that multiply to produce 6 and add together to produce 5. Lets try and factorise 6 first. The pairs that we obtain are:

1,6

2,3

Thats all. These pairs are all factors of 6. Lets try and spot if any of them add up to produce 5!

The pair 2 and 3 do! So they multiply to produce 6 and add together to produce 5. We have sucessfully found our roots to the quadratic equation. So the last step is to rewrite it in the form (x + 2)(x + 3) = 0 if needed.

if our roots were -2 and -3, we would have (x + (-2))(x + (-3)) = 0. Which would be rewritten as (x - 2)(x - 3) = 0.

Please note that sometimes the numbers aren't nice enough to use this method. In which case, the quadratic formula would be our best bet. 

Tarun S. GCSE Maths tutor, A Level Maths tutor, Mentoring HTML & CSS ...

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