How do I solve a quadratic equation by factorising?

MYTUTOR SUBJECT ANSWERS

Answers / Maths / GCSE / How do I solve a quadratic equation by factorising?

748 views

How do I solve a quadratic equation by factorising?

A quadratic equation is one that includes x²as 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

562 SUBJECT SPECIALISTS

Mabast H. GCSE Physics tutor, A Level Physics tutor, IB Physics tutor...

View profile

£18 /hr

Mabast H.

Degree: Physics (Bachelors) - Imperial College London University

Subjects offered:Maths, Physics+ 3 more

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

MyTutor guarantee

Save profile

Edward H. A Level Geography tutor, GCSE Geography tutor, IB Geography...

View profile

£36 /hr

Edward H.

Degree: Geography (Masters) - Oxford, Balliol College University

Subjects offered:Maths, Music+ 7 more

“I am a Geography student at Oxford University, but I also have experience tutoring in Maths, Chemistry, English, French, Mandarin Chinese, and Music. I am an ethusiastic and dedicated individual, tailoring my classes to the needs of ea...”

4.9

42 reviews | 144 completed tutorials

Save profile

Akhil P. GCSE Biology tutor, A Level Biology tutor, GCSE Chemistry tu...

View profile

£20 /hr

Akhil P.

Degree: Medicine (Bachelors) - Imperial College London University

Subjects offered:Maths, Physics+ 6 more

“First Year Medical student at Imperial College. Studies all 3 sciences and Maths at A-levels and did an EPQ(4 A*s and an A)”

5.0

4 reviews | 8 completed tutorials

Save profile

See more GCSE Maths tutors

About the author

Shannon G.

Currently unavailable: for regular students

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

Subjects offered:Maths, Science+ 2 more

“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!”

4.9

69 reviews | 239 completed tutorials

Save profile

Version:	3.47.1
Build:	245b6290c38f
Time:	2017-07-12T13:15:28Z

MYTUTOR SUBJECT ANSWERS

How do I solve a quadratic equation by factorising?

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

562 SUBJECT SPECIALISTS

About the author

You may also like...

Posts by Shannon

Other GCSE Maths questions

One-to-one help is at your fingertips