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Unit 24Solving Quadratic Equations

Presentation 1 Factorisation

Presentation 2 Using the formula

Presentation 3 Summary of Number of Solutions

Presentation 4 Completing the Square

Unit 24Solving Quadratic Equations

- 24.1 Factorisation

A quadratic equation is of the form and can be

solved easily if it factorises.

Example 3 Solve Solution Factorising so

either or

Example 4 Solve Solution Factorising so

there is only one (repeated) solution

Example 1 Solve Solution Factorising so

either or solution or

Example 2 Solve Solution Factorising so

either or

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Unit 24Solving Quadratic Equations

- 24.2a Using the formula

There is a formula to solve the quadratic

equation The solution is given by

Solution Here so

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Example 1 Using the formula, solve the quadratic

equation Giving the solution correct to two

decimal places.

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or

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or

To 2 d.p.

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Unit 24Solving Quadratic Equations

- 24.2b Using the formula

Again, using the formula to solve the quadratic

equation Example 2 Solve the quadratic

equation Solution Here , , and

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There is only one distinct root as

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Unit 24Solving Quadratic Equations

- 24.2c Using the Formula

Again, using the formula to solve the quadratic

equation Example 3 Solve the quadratic

equation Solution Here , , and

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This has no solution as

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This is the case when

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Unit 24Solving Quadratic Equations

- Summary of Number of Solutions

A quadratic equation can have 2,1 or 0

solutions. The following graphs illustrate these

graphically and show how the number of solutions

depend on the sign of which is part of the

quadratic formula.

No. of solutions 0 See previous Example 3

No. of solutions 1 See previous Example 2

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No. of solutions 2 See previous Example 1

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Unit 24Solving Quadratic Equations

- 24.4 Completing the Square

The formula for solving a quadratic equation

comes from completing the square. Example Expres

s in the form when a, p and q are real

numbers. Solution

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So comparing coefficients,

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Extension What is the minimum value of ?

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This is and it occurs when

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Thus

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For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

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