How do I find the root of a quadratic equation?

Usually the easiest way to find the root of a quadratic is to factorise it so you have something a form similar to - (x+2)(x-1)=0.

From here you need to find a value for x that makes each bracket equal to zero. Here we can see our answers are x = 1 and x = -2.

If the equation cannot be factorised our backup method that is slightly more complicated but always correct is to use the quadratic equation. 

This is given as x = (-b ± (b2-4ac)1/2)/2a,

Where a, b and c come from your original quadratic as ax2+bx+c. 

Nicky F. A Level Maths tutor, GCSE Maths tutor, GCSE Spanish tutor, A...

2 years ago

Answered by Nicky, an A Level Maths tutor with MyTutor

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


PremiumMatthew D. A Level Further Mathematics  tutor, A Level Maths tutor, G...
View profile
£26 /hr

Matthew D.

Degree: Maths and Philosophy (Masters) - Durham University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“ I will make sure I am familiar with your specific exam board, and questions beyond this can of course be pursued in a tutorial too”

Sophie K. GCSE Maths tutor, Mentoring -Personal Statements- tutor, A ...
View profile
£20 /hr

Sophie K.

Degree: Mathematics (Bachelors) - Birmingham University

Subjects offered: Maths, History+ 2 more

English Literature
-Personal Statements-

“About Me Hi, I'm Sophie and I'm a Maths student at the University of Birmingham. I have always had a passion for maths due to the satisfaction you get from obtaining the one correct answer and the amount of real world applications it ...”

Aidan T. GCSE Maths tutor, A Level Maths tutor
View profile
£22 /hr

Aidan T.

Degree: Chemical Engineering (Masters) - Edinburgh University

Subjects offered: Maths


“Hi! I am currently studying Chemical Engineering at The University of Edinburgh. I tutor in Edinburgh 6-7 times per week currently, and joined MyTutor as a way of sumplimenting that with the convenience of being able to stay in my ...”

About the author

Nicky F. A Level Maths tutor, GCSE Maths tutor, GCSE Spanish tutor, A...
View profile

Nicky F.

Currently unavailable: for regular students

Degree: Physics (Masters) - Durham University

Subjects offered: Maths, Spanish+ 2 more

-Personal Statements-

“Experienced Tutor from Durham University. Targeted and unique help with Maths, Physics or Spanish. ”

You may also like...

Posts by Nicky

How do I find the root of a quadratic equation?

When should I use the preterite and the imperfect form of the past tense?

Other A Level Maths questions

How do you intergrate ln(x)?

Find the all the angles of a triangle with side lengths of 8cm, 11cm and 11cm.

Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.

How do you find the minimum of the equation sin^2(x) + 4sin(x)?

View A Level Maths tutors


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