Solving Quadratics using a Calculator (Cambridge (CIE) IGCSE International Maths)

Revision Note

Jamie Wood

Expertise

Maths

Solving Quadratics using a Calculator

How do I solve quadratic equations using my calculator?

  • Your graphic display calculator is able to solve quadratic equations

  • Within the menu you will find an option for solving a polynomial

    • This may be within the equation solver section on some models

  • Select the degree or order of polynomial you are solving

    • When solving a quadratic, the degree or order is 2

  • Type in the coefficients of the quadratic you are solving

    • This is usually in the format

      • a subscript 2 x squared plus a subscript 1 x plus a subscript 0 equals 0 or

      • a x squared plus b x plus c equals 0

    • E.g. To solve x squared plus 6 x minus 4 equals 0

      • a subscript 2 equals 1 space comma space a subscript 1 equals 6 space comma space a subscript 3 equals negative 4 or

      • a equals 1 space comma space b equals 6 space comma space c equals negative 4

    • You must therefore rearrange the equation you are solving to this format ( ... = 0)

  • Then press enter or solve to view the solutions

Should I round my answers?

  • Your graphic display calculator will present answers in exact form where possible

    • E.g. negative 3 plus square root of 13 space rather than 0.6055512755...

      • Your calculator will be able to switch between the exact form and a decimal

    • If there is further working to be done using this answer

      • it is best to keep it in an exact form

    • If the solutions to the quadratic are the final answers for the question

      • check the question to see if it requests an exact answer

      • or a decimal approximation (e.g. to three significant figures)

Should I show my working when using a calculator to solve a quadratic?

  • In a calculator paper it is expected that you use your calculator to solve quadratic equations

  • Therefore you do not need to show working (such as using the quadratic formula)

  • However, you should write down:

    • The equation you are entering into your calculator (and any prior rearranging)

    • Both solutions found by your calculator

      • In exact form where possible

  • This will ensure you receive as many method marks as possible, in case of an error

Exam Tip

Solving a quadratic on your calculator can also help factorise a quadratic:

  • If the solutions to a quadratic equation are x equals negative 3 and x equals 2

  • Then the equation can be written as open parentheses x plus 3 close parentheses open parentheses x minus 2 close parentheses equals 0

Worked Example

Use your calculator to solve the equation 10 x equals 19 minus 6 x squared giving your solutions to four significant figures.

Rearrange the equation to the form a x squared plus b x plus c equals 0

table row cell 10 x end cell equals cell 19 minus 6 x squared end cell row cell 6 x squared plus 10 x end cell equals 19 row cell 6 x squared plus 10 x minus 19 end cell equals 0 end table

On your calculator, enter the menu and select the polynomial solver
Enter the coefficients of 6, 10 and -19, and solve

Write down the exact solutions

x subscript 1 equals fraction numerator negative 5 plus square root of 139 over denominator 6 end fraction
x subscript 2 equals fraction numerator negative 5 minus square root of 139 over denominator 6 end fraction

The question requests the answers to four significant figures
Find the decimal approximations to the solutions on your calculator

x subscript 1 equals 1.131637687...
x subscript 2 equals negative 2.798304354...

Round to four significant figures

bold italic x subscript bold 1 bold equals bold 1 bold. bold 132
bold italic x subscript bold 2 bold equals bold minus bold 2 bold. bold 798

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Jamie Wood

Author: Jamie Wood

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.