651 views

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

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.

1 year ago

Answered by Tarun, a GCSE Maths tutor with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 627 SUBJECT SPECIALISTS

£24 /hr

Degree: Mathematical and Theoretical Physics (Masters) - Oxford, Merton College University

Subjects offered:Maths, Science+ 5 more

Maths
Science
Physics
Further Mathematics
Chemistry
.MAT.
-Personal Statements-

“Mathematics and Theoretical Physics, University of Oxford. I enjoy sharing my experience and enthusiasm in Maths with those who could do with some help”

£18 /hr

Degree: Physics (Bachelors) - Imperial College London University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
Chemistry
-Personal Statements-

“Undergraduate Physicist with lots of experience in teaching in different fields and age groups, looking to instil a passion for learning into students.”

£36 /hr

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Italian
Further Mathematics
Economics

“Exam Time! I can provide a rapid revision class in any maths module which will test your son or daughter in all the fundamentals”

Currently unavailable: until 30/11/2016

Degree: Computer Science (Bachelors) - Imperial College London University

Subjects offered:Maths

Maths

“I am very passionate about the study of mathematics and enjoy breaking down complex problems into simple solutions whilst explaining the process of doing so. I adapt my teaching methods to the each student to try and maximise their gr...”

MyTutor guarantee

### You may also like...

#### Posts by Tarun

How can i solve the following simultaneous equations? 5x + y = 4 and 3x + 2y = 5?

How do i differentiate the equation y = x^2 + 6x + 2 with respect to x.

How do i factorise 20 + 10x?

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

#### Other GCSE Maths questions

Solve X^2 +13X+48=12

How do I expand (x+a)(x+b)? (plus example)

Solve the simultaneous equations: 3a + 2b = 17 and 4a - b = 30

How to factorise a simple linear equation such as '9Y + 6'

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.