math unit24 solving quadratic equations
TRANSCRIPT
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
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
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A quadratic equation is of the formand can be solved easily if it factorises.
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Unit 24Solving Quadratic Equations
24.2a Using the formula
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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 ? ? ?
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To 2 d.p. or
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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
There is only one distinct root as
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Unit 24Solving Quadratic Equations
24.2c Using the Formula
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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
This is the case when
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Unit 24Solving Quadratic Equations
Summary of Number of Solutions
No. of solutions = 0See previous Example 3
No. of solutions = 2See previous Example 1
No. of solutions = 1See 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 ofwhich is part of the quadratic formula.
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Unit 24Solving 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.ExampleExpress in the form when a, p and q are real numbers.Solution
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So comparing coefficients,
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ExtensionWhat is the minimum value of ?
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