MYTUTOR SUBJECT ANSWERS

752 views

How to find the roots of a Quadratic Equation by Factorising?

Suppose you have a quadratic equation: x+ 5x + 6

You are told it has TWO REAL ROOTS and you are to find them.

The factorised quadratic with two roots will look like this:

(x+a)(x+b)

Where a and b are real numbers (any positive or negative number really)

As this is just another form of the original equation we can say they are equal:

(x+a)(x+b) = x+ 5x + 6

 

If you mulitply out the brackets using the FOIL (First, Outside, Inside, Last) rule you get:

x2 + xa + xb + ab = x+ 5x + 6

It's clear the x2 terms cancel out, and if we equate the x terms and the number terms, we are left with

xa + xb = 5x        and  ab= 6

x(a+b) = 5x                  a x b = 6

a + b = 5

So now we must use this information to find a and b.

The factors of 6 are:

6 and 1 

3 and 2

Of those factors, the pair which adds to 5 are 3 and 2.

so a = 3 and b = 2

Now we must check the signs of the factorised equation to check when we multiply ot the bracket we get the original equation again.... 

(x+3)(x+2) = x2 + 5x + 6 - CORRECT

Now we use this to find the roots, i.e. the x coordinates were y = 0 

so therefore we make our factorised quadratic equal to 0

(x+3)(x+2)=0

If two things multiplied together = 0, then at least one of them must equal 0...

x+3 = 0 ==> x = -3

OR

x+2 = 0 ==> x = -2

 

We can check the roots are corrects by replacing a and b with the x terms in the original equation and it should equal 0 for both a and b

We now have our roots...

x = -3 

and x = -2

Joshua F. GCSE Chemistry tutor, GCSE Maths tutor, A Level Maths tutor...

3 years ago

Answered by Joshua, a GCSE Maths tutor with MyTutor


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

623 SUBJECT SPECIALISTS

£30 /hr

Helen M.

Degree: Law (Bachelors) - Durham University

Subjects offered:Maths, Business Studies+ 2 more

Maths
Business Studies
.LNAT.
-Personal Statements-

“Durham law graduate with four years tutoring experience in a wide range of subjects. ”

£24 /hr

Sioned D.

Degree: Law (Bachelors) - University College London University

Subjects offered:Maths, History+ 4 more

Maths
History
English
Biology
.LNAT.
-Personal Statements-

“Hello! I'm a Cambridge University Masters student and UCL Law graduate with a great deal of tutoring experience in English, Maths, Sciences and Entrance Exams.”

Luke S. GCSE History tutor, 13 Plus  History tutor, A Level History t...
£18 /hr

Luke S.

Degree: Philosophy, Politics and Economics (Bachelors) - Oxford, Worcester College University

Subjects offered:Maths, Spanish+ 4 more

Maths
Spanish
Philosophy and Ethics
History
Economics
.TSA. Oxford.

“I am an aspiring teacher, with a clear and analytic approach to tutoring that comes from an extensive and varied educational background.”

About the author

Joshua F.

Currently unavailable: no new students

Degree: Chemical Engineering w/ industrial experience (Masters) - Manchester University

Subjects offered:Maths, Science+ 2 more

Maths
Science
Physics
Chemistry

“First Year Chemical Engineering student at Manchester. Current BP STEM Scholar. Science and maths can be complicated - but everything can be simplified and easy to understand”

MyTutor guarantee

|  1 completed tutorial

You may also like...

Other GCSE Maths questions

Simplify the expression: 3x + 2y -7x + c + y

Each day Chen buys pasta or a sandwich. Where Pasta costs £3.20 and Sandwich costs £2.75. For 45 days, the relative frequency of Chen buying a sandwich was one fifth. Altogether, how much did he pay?

How can you find the integral of x^-1

What can I do to revise maths?

View GCSE Maths tutors

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

mtw:mercury1:status:ok