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


Sahil M. A Level Biology tutor, GCSE Biology tutor, A Level Chemistry...
£22 /hr

Sahil M.

Degree: Medicine (Bachelors) - Manchester University

Subjects offered:Maths, Spanish+ 3 more

-Medical School Preparation-

“Hello! My name is Sahil and I am currently a medical student at the University of Manchester. I am really looking forward to tutoring you in Spanish, Chemistry, Biology or Maths as well as trying to help you during the difficult proce...”

£20 /hr

Madeleine N.

Degree: Maths and Physics (Masters) - Durham University

Subjects offered:Maths, Spanish+ 2 more

Further Mathematics

“Enthusiastic student, studying Maths and Physics at Durham university: keen to work hard with students to improve their results.”

£22 /hr

Sophie H.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths


“I’ll help anyone finding maths hard. I still struggle now, it's not meant to be easy! Be at my tutorial or (c^2-a^2) <- a maths joke, I apologise.”

About the author

£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 do you differentiate y=sin(cos(x))?

How would you differentiate f(x) = 2x(3x - 1)^2 using the chain rule?

The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.

Pushing a mass up a slope and energy

View A Level 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