MYTUTOR SUBJECT ANSWERS

832 views

How do I solve a quadratic equation by factorising?

 A quadratic equation is one that includes xas the highest power of x. Factorising is achieved in 3 steps. Let’s consider the example x2-3x-3=1

1) Put the equation into the form ax2+bx+c=0

x2-3x-4=0

2) Factorise

We need two numbers that

- add together to get -3

- Multiply together to get -4

-4x1=-4 and -4+1=-3

Thus, factorising gives (x-4)(x+1)=0

3) Solve the equation!

If two numbers are multiplied together to give 0, one of them must be 0. Thus:

x-4=0 and x=4

x+1=0 and x=-1

The equation has been solved

Additional points:

- This technique can be applied to finding the points of intersection on the x axis for a quadratic graph. For example, y=x2-3x-4. At the x axis, y=0 so you can work out x as above.

- Harder quadratic equations can also be solved by factorising. For example when a isn't 1. 

2x2 + 7x + 3=0

Find two numbers that multiply to give 2x3 (6) and add to give 7. In this case, 6 and 1.

Split 7x into 6x +x

2x2 + 6x+x + 3=0

Factorise each part by taking out a common factor. 

2x(x+3)+1(x + 3)=0

The sames as

(2x+1)(x+3)=0

thus x = -1/2 or x=-3

Practice questions

1. Solve by factorising

x2 + 6x + 8=0

x2 – 8x + 16 = 0

2. Find the points of intersection with the x axis for

y=x2 – 14x + 48

and sketch this function

Shannon G. GCSE Biology tutor, A Level Biology tutor, GCSE Chemistry ...

2 years ago

Answered by Shannon, a GCSE Maths tutor with MyTutor


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

803 SUBJECT SPECIALISTS

£18 /hr

Rhiannon M.

Degree: Environmental Geoscience (Bachelors) - Durham University

Subjects offered:Maths, Geology+ 2 more

Maths
Geology
Geography
Chemistry

“Third year Earth Sciences student at Durham; specialise in geochemistry and tutor in Earth sciences, Chemistry and Maths”

Trusted by schools

|  4 completed tutorials

£18 /hr

Rachel H.

Degree: Veterinary Medicine (with Intercalated Year) (Bachelors) - Royal Veterinary College University

Subjects offered:Maths, Science+ 5 more

Maths
Science
Human Biology
English
Chemistry
-Personal Statements-

“Fourth year vet student and self-proclaimed science nerd, offering personalised tuition in the sciences, maths and English at all levels from 11+ to A Level/IB”

MyTutor guarantee

£20 /hr

Ruth N.

Degree: Economics (Bachelors) - Cambridge University

Subjects offered:Maths, Economics+ 2 more

Maths
Economics
-Personal Statements-
-Oxbridge Preparation-

“Economics Graduate from Cambridge, wanting to share my passion for the discipline”

About the author

PremiumShannon G. GCSE Biology tutor, A Level Biology tutor, GCSE Chemistry ...

Shannon G.

Currently unavailable: for regular students

Degree: Biomedical Science (Bachelors) - Oxford, Oriel College University

Subjects offered:Maths, Science+ 2 more

Maths
Science
Chemistry
Biology

“Hello, I'm Shannon. I am an Oxford biomedical student and a passionate tutor. I am keen to offer support to any student studying chemistry, biology or maths with a love of learning!”

You may also like...

Posts by Shannon

How do I find the turning points of a curve?

How do I solve a quadratic equation by factorising?

How does meiosis achieve genetic diversity?

What is a coordinate bond?

Other GCSE Maths questions

Solve the two simultaneous equations: 2x - 5y = 11 and 3x + 2y = 7

Solve the simultaneous equations: 4x + y = 25, x - 3y = 16

How can I tell if two lines are perpendicular from the equations?

Solve the quadratic equation x^2 + 3x + 2 = 0, by factorisation.

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