How to solve a quadratic equation?

 How to solve a quadratic equation?

While learning mathematics, you will often meet quadratic equations. These equations serve a mathematical way to say that a certain equation, which may resemble a real-life problem, may have more than one solution.

Identifying quadratics

The general formula of the quadratic is ax2 + bx + c = 0, but it is very rare that a quadratic equations appears in its very bare form. In exams, they often like to hide it in certain ways, for example:

·       5*cos2(x) + 3 = 2 *cos(x), where you can introduce a new variable y, and solve for y. Remember that you still need to solve for y = cos(x) after that.

·       Or basically they can use any trigonometric function or logarithm to hide a quadratic.

·       Often, a higher degree equation can be simplified to a quadratic, for example x6 + 3x3 + 2 = 0, where you can introduce a new variable, just like in the previous example.

Methods to solve a quadratic

The general formula for solving the quadratic is x = (-B + or – SQRT(B2 – 4AC))/2A

Where A, B,C are the coefficients of the equations. If you don’t know what a coefficient is, it is basically the number before the unknowns in the equation. Often you see can see that e.g. x2 doesn’t have a number before it, but that simply means that its coefficient is 1.

Also, you can use the Vieta-formulas to solve a quadratic, which are relationships between the coefficients of the equation and its roots (solutions).

-B/A = the two roots added together

C/A = the two roots multiplied together

I recommend that you get comfortable with these relationships, because these Vieta-formulas in some way remain true at higher degree equations.

Another method to solve a quadratic is, completing the square, for example x2 + 2x + 1 = (x+1)2, so we can know that -1 is the only solution to our quadratic equation.

Bence H. A Level Maths tutor, A Level Physics tutor, A Level Chemistr...

2 years ago

Answered by Bence, an A Level Maths tutor with MyTutor

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


Constantinos C. GCSE Maths tutor, GCSE Biology tutor, GCSE Physics tu...
View profile
£20 /hr

Constantinos C.

Degree: MRes Ecology, Evolution and Conservation (Masters) - Imperial College London University

Subjects offered: Maths, Physics+ 3 more

-Personal Statements-

“I am a Biology graduate, and thus have the necessary critical thinking and learning skills that I can transfer to you. I am now a student in a research-based Masters at Imperial College. During university, I have worked as a mentor an...”

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”

Samuel H. A Level Maths tutor, A Level Physics tutor, GCSE Maths tuto...
View profile
£22 /hr

Samuel H.

Degree: Mathematics with International Study (Masters) - Exeter University

Subjects offered: Maths, Physics


“I have not only been able to teach AS Level students how to solve mechanics problems; I helped them understand the concepts behind the problems”

About the author

Bence H. A Level Maths tutor, A Level Physics tutor, A Level Chemistr...
View profile
£20 /hr

Bence H.

Degree: Biomedical Engineering (Bachelors) - Imperial College London University

Subjects offered: Maths, Physics+ 2 more


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

How does one find the inverse of a non-singular 3x3 matrix A?

What qualifications and experience do you have at this level?

How would you differentiate ln(sin(3x))?

What is the second derivative used for?

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