Quadratic Formula (SQA National 5 Maths): Revision Note

Solving a quadratic equation using the quadratic formula

What is the quadratic formula?

• A quadratic equation has the form ax² + bx + c = 0 (where a ≠ 0)

  • you need "= 0" on one side

• The quadratic formula is a formula that gives both solutions to a quadratic equation:

How do I use the quadratic formula to solve a quadratic equation?

• Read off the values of a, b and c from the equation

• Substitute these into the formula

  • Write this line of working in the exam

  • Put brackets around any negative numbers being substituted in

• To solve 2x² - 8x - 3 = 0 using the quadratic formula:

  • a = 2, b = -8 and c = -3

  • 

  • Either type this into a calculator or simplify by hand

    • Type it once using + for  ± then again using - for  ±

  • The solutions are x = 4.345207... or x = -0.345207....

    • To 3 decimal places: x = 4.345 or x = -0.345

    • To 3 significant figures: x = 4.35 or x = -0.345

How do I write the solutions in an exact (surd) form?

• It is also possible to give answers in an exact (surd) form

• For the example above, work out the number under the square root sign

  • Be careful with negatives!

    • 

  • Now take the square root of this number and use surd rules to simplify

    • 

  • Substitute this back into the formula and simplify

    • 

    • The solutions in exact (surd) form are or

• Calculators that can solve quadratics will give solutions in exact (surd) form

Can I use my calculator to solve quadratic equations?

• If your calculator solves quadratic equations, use it to check your final answers

  • But a correct method and working must still be shown

• If your calculator gives you solutions with terms containing , these are "complex" and are not what you are looking for

  • You may have made a mistake entering the quadratic equation

  • Or the equation may not have any real number solutions