IBMathsDPAnalysis & Approaches (AA)HLRevision Notes2. FunctionsQuadratic Functions & GraphsSolving Quadratics

Solving Quadratics (DP IB Analysis & Approaches (AA)) : Revision Note

Dan Finlay

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DP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SL

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Solving Quadratic Equations

How do I decide the best method to solve a quadratic equation?

  • A quadratic equation is of the form a x squared plus b x plus c equals 0

  • If it is a calculator paper then use your GDC to solve the quadratic

  • If it is a non-calculator paper then...

    • you can always use the quadratic formula

    • you can factorise if it can be factorised with integers

    • you can always complete the square

How do I solve a quadratic equation by the quadratic formula?

  • If necessary rewrite in the form a x squared plus b x plus c equals 0

  • Clearly identify the values of a, b & c

  • Substitute the values into the formula

    • x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction 

      • This is given in the formula booklet

  • Simplify the solutions as much as possible

How do I solve a quadratic equation by factorising?

  • Factorise to rewrite the quadratic equation in the form a left parenthesis x minus p right parenthesis left parenthesis x minus q right parenthesis equals 0

  • Set each factor to zero and solve

    • x minus p equals 0 rightwards double arrow x equals p

    • x minus q equals 0 rightwards double arrow x equals q

How do I solve a quadratic equation by completing the square?

  • Complete the square to rewrite the quadratic equation in the form a open parentheses x minus h close parentheses squared plus k equals 0

  • Get the squared term by itself

    • open parentheses x minus h close parentheses squared equals negative k over a

  • If open parentheses negative k over a close parentheses is negative then there will be no solutions

  • If open parentheses negative k over a close parentheses is positive then there will be two values for x minus h

    • x minus h equals plus-or-minus square root of negative k over a end root

  • Solve for x

    • x equals h plus-or-minus square root of negative k over a end root

Examiner Tips and Tricks

  • When using the quadratic formula with awkward values or fractions you may find it easier to deal with the " b squared minus 4 a c " (discriminant) first

    • This can help avoid numerical and negative errors, improving accuracy

Worked Example

Solve the equations:

a) 4 x squared plus 4 x minus 15 equals 0.

2-2-3-ib-aa-sl-quadratic-equations-a-we-solution

b) 3 x squared plus 12 x minus 5 equals 0.

2-2-3-ib-aa-sl-quadratic-equations-b-we-solution

c) 7 minus 3 x minus 5 x squared equals 0.

2-2-3-ib-aa-sl-quadratic-equations-c-we-solution

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Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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