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Unit 24 Solving Quadratic Equations

Unit 24 Solving Quadratic Equations. Unit 24 Solving 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

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Unit 24 Solving Quadratic Equations

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  1. Unit 24Solving Quadratic Equations

  2. Unit 24Solving Quadratic Equations 24.1 Factorisation

  3. 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 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

  4. Unit 24Solving Quadratic Equations 24.2a Using the formula

  5. There is a formula to solve the quadratic equation The solution is given by Solution Here so ? ? ? Example 1 Using the formula, solve the quadratic equation Giving the solution correct to two decimal places. ? ? ? ? ? ? ? ? ? ? or ? ? or To 2 d.p. ? ?

  6. Unit 24Solving Quadratic Equations 24.2b Using the formula

  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. Unit 24Solving Quadratic Equations 24.2c Using the Formula

  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. Unit 24Solving Quadratic Equations Summary of Number of Solutions

  11. 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 ? ? No. of solutions = 2 See previous Example 1 ?

  12. Unit 24Solving Quadratic Equations 24.4 Completing the Square

  13. 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, ? ? Extension What is the minimum value of ? ? ? ? ? ? This is and it occurs when ? ? Thus ?

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