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Calculus 3.4 Manipulate real and complex numbers and solve equations AS 90638.

Published byCameron Hicks Modified over 9 years ago

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Presentation on theme: "Calculus 3.4 Manipulate real and complex numbers and solve equations AS 90638."— Presentation transcript:

1 Calculus 3.4 Manipulate real and complex numbers and solve equations AS 90638

2 Recognising terms

3

4

5

6 Worksheet 1

7 Quadratics General formula:

8 Example 1. Solving for the roots (i.e. y = 0) Method 1: Factorising

9 Method 2: Quadratic Formula

10 Method 3: Graphics Calculator Equation Mode F2: Polynomial Degree: 2 (F1) Enter 1, -2, -3 Solve (F1)

11 Equation has 2 real solutions x = 3, -1

12 Example 2 Method 1: Factorize

13 Method 2: Quadratic Formula

14 Equation has two equal real solutions: x = 3, 3

15 Example 3 Equation cannot be factorised.

16 Using quadratic formula Equations has no real solutions

17 Equation has no real roots.

18 Forming quadratic equations from 2 solutions. If solutions are

19 Example 1 Quadratic equation is

20 Example 2 Quadratic equation is

21 Example 3

22 Factorise Form the quadratic

23 Solve Sketch the graph

24 Solve Sketch the graph

25 Completing the square Half the coefficient of x Subtract this value squared

26 Completing the square Half the coefficient of x Subtract this value squared

27 Completing the square Take out the 2

28 Completing the square Half the coefficient of x Subtract this value squared

29 Completing the square Half the coefficient of x Subtract this value squared

30 Completing the square Take out the -3

31 Completing the square Half the coefficient of x Subtract this value squared

32 Completing the square Half the coefficient of x Subtract this value squared

33 Worksheet 2

34 Factor Remainder Theorem

35 Division of polynomials Write down the coefficients 2 3 -29 20 Solve 2 2x 4 7 14 -15 -30 -10 Divide

36 Substituting x = 2 i.e. substituting into the original gives us the remainder

37 Example 2 Write down the coefficients 3 -2 -7 -2 Solve 3x -3 -5 5 -2 2 0 A remainder of 0 means is a factor and -1 is a solution

38 Substituting x = -1 When -1 is substituted, remainder is 0

39 Factorising the quadratic gives

40 To factorise a cubic first find a value that will give a remainder of 0.

41

42

43 Create the cubic by equating coefficients

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