How do you know when to use the quadratic formula in a maths exam question.

In most examination questions it won’t always tell you when to use the quadratic formula. So you need to be able to identify which quadratic equations require the use of the quadratic formula.

First of all, you will need to be able to identify what a quadratic equation looks like. A quadratic equation takes the form ax² + bx  + c = 0. The highest power of x in a quadratic equation is of order 2.

Once you have identified that the equation is a quadratic you now need to solve it. The easiest way to solve a quadratic is by factorisation. However, if the question asks you to round your answer to an appropriate degree of accuracy, or leave your answers as exact numbers (in the form a ± √b) then this is a clear indication that the quadratic equation cannot be factorised. If this is the case, then you  shouldn’t try to factorise the quadratic equation. Instead,  plug your a,b and c values straight into the quadratic formula.

In each of the examples shown below, say whether or not, you would use the quadratic formula to solve the equation:

Question 1

Solve x³ = 15 to 1 decimal place.


No, you wouldn’t use the quadratic formula as it’s a cubic equation and not a quadratic equation.

Question 2

Solve x² -3x – 41 = 0. Give your answers to 3 significant figures.


Yes, as the equation is quadratic and it’s asking you to round off your answer.

Question 3

Solve x² + 5x + 4 = 0.

No, as the quadratic can be factorised.

Question 4

Solve x² - x – 11. Write your answers in the form a ± √b.

Yes, as the equation is quadratic and it asks you to write the solutions as exact answers.  

To summarise, if the equation is a quadratic and it’s asking you to round off your answer, then always use the quadratic formula to find your solutions.

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catman3000 profile image

catman3000 5 years ago from England, UK Author

Yes, completing the square can be used to solve a quadratic equation. Again, I would use this method when the quadratic cannot be factorised as an alternative to the quadratic formula.

James Agbogun profile image

James Agbogun 5 years ago

Catmann3000, there should be a third method called "completing the square method". Am wondering when it can be the option for solving a quadratic problem. Thanks!

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