Solving Quadratics using a Calculator (Cambridge International IGCSE 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

    • $a_{2}x^{2}+a_{1}x+a_{0}=0$ or
    • $ax^{2}+bx+c=0$

  • E.g. To solve $x^{2}+6x-4=0$

    • $a_{2}=1,a_{1}=6,a_{3}=-4$ or
    • $a=1,b=6,c=-4$

  • 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. $-3+\sqrt{13}$ 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 Hint Solving a quadratic on your calculator can also help factorise a quadratic:

• If the solutions to a quadratic equation are $x=-3$ and $x=2$
• Then the equation can be written as $( x + 3 ) ( x - 2 ) = 0$

Worked Example Use your calculator to solve the equation $10x=19-6x^{2}$ giving your solutions to four significant figures.

Rearrange the equation to the form $ax^{2}+bx+c=0$

$\begin{gathered} 10 x & = 19 - 6 x^{2} \\ 6 x^{2} + 10 x & = 19 \\ 6 x^{2} + 10 x - 19 & = 0 \end{gathered}$

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

$x_{1}=\frac{-5+\sqrt{139}}{6}\,x_{2}=\frac{-5-\sqrt{139}}{6}$

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

$x_{1}=1.131637687...\,x_{2}=-2.798304354...$

Round to four significant figures

$x_{1}=1.132\,x_{2}=-2.798$