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Unit 24
Solving Quadratic Equations
Presentation 1 Factorisation
Presentation 2 Using the formula
Presentation 3 Summary o...
Unit 24
Solving Quadratic Equations
24.1 Factorisation
Example 1
Solve
Solution
Factorising
so either or
solution or
Example 3
Solve
Solution
Factorising
so either or
Example 2
...
Unit 24
Solving Quadratic Equations
24.2a Using the formula
?
There is a formula to solve the quadratic equation
The solution is given by
Example 1
Using the formula, solve the quadr...
Unit 24
Solving 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
The...
Unit 24
Solving Quadratic Equations
24.2c Using the Formula
?
?
?
Again, using the formula to solve the quadratic
equation:
Example 3
Solve the quadratic equation
Solution
Here , , a...
Unit 24
Solving Quadratic Equations
Summary of Number of Solutions
No. of solutions = 0
See previous Example 3
No. of solutions = 2
See previous Example 1
No. of solutions = 1
See previous ...
Unit 24
Solving Quadratic Equations
24.4 Completing the Square
This is and it occurs when
The formula for solving a quadratic equation comes from
completing the square.
Example
Express ...
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Math unit24 solving quadratic equations

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Solving Quadratic Equations

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Math unit24 solving quadratic equations

  1. 1. Unit 24 Solving Quadratic Equations Presentation 1 Factorisation Presentation 2 Using the formula Presentation 3 Summary of Number of Solutions Presentation 4 Completing the Square
  2. 2. Unit 24 Solving Quadratic Equations 24.1 Factorisation
  3. 3. Example 1 Solve Solution Factorising so either or solution or Example 3 Solve Solution Factorising so either or Example 2 Solve Solution Factorising so either or Example 4 Solve Solution Factorising so there is only one (repeated) solution? ? ? A quadratic equation is of the form and can be solved easily if it factorises. ? ? ? ? ?? ? ?? ? ? ? ?
  4. 4. Unit 24 Solving Quadratic Equations 24.2a Using the formula
  5. 5. ? There is a formula to solve the quadratic equation The solution is given by Example 1 Using the formula, solve the quadratic equation Giving the solution correct to two decimal places. Solution Here so? ? ? ? ? ? ? ? ? ? ? or To 2 d.p. or ? ??? ?
  6. 6. Unit 24 Solving Quadratic Equations 24.2b Using the formula
  7. 7. Again, using the formula to solve the quadratic equation: Example 2 Solve the quadratic equation Solution Here , , and There is only one distinct root as ? ?? ? ?? ?? ? ?? ?
  8. 8. Unit 24 Solving Quadratic Equations 24.2c Using the Formula
  9. 9. ? ? ? Again, using the formula to solve the quadratic equation: Example 3 Solve the quadratic equation Solution Here , , and ? ? ? This has no solution as This is the case when ??? ? ?
  10. 10. Unit 24 Solving Quadratic Equations Summary of Number of Solutions
  11. 11. No. of solutions = 0 See previous Example 3 No. of solutions = 2 See previous Example 1 No. of solutions = 1 See previous Example 2 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. ?? ?
  12. 12. Unit 24 Solving Quadratic Equations 24.4 Completing the Square
  13. 13. This is and it occurs when The formula for solving a quadratic equation comes from completing the square. Example Express in the form when a, p and q are real numbers. Solution ? ? ? ? ? So comparing coefficients, ? ? ? ? ? ?Thus Extension What is the minimum value of ? ??

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