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Surds and Quadratics: Operations and Solutions

Learn about adding, subtracting, multiplying, and dividing surds, as well as solving quadratic equations using different methods, including factorising and the quadratic formula. Understand real and complex solutions. Worksheets provided.

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Surds and Quadratics: Operations and Solutions

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  1. Surds and Quadratics AS 91577

  2. Surds • Adding • Subtracting • Multiplying • Dividing

  3. Adding and subtracting surds

  4. Multiplying SurdsExample 1:

  5. Multiplying SurdsExample 2:

  6. Dividing surds(Rationalising)Example 1 Multiply top and bottom by

  7. Dividing surds(Rationalising)Example 2 Multiply top and bottom by

  8. Recognising terms

  9. Worksheet 1

  10. Quadratics General formula:

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

  12. Method 2: Quadratic Formula

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

  14. Equation has 2 real solutionsx = 3, -1

  15. Example 2 Method 1: Factorize

  16. Method 2: Quadratic Formula

  17. Equation has two equal solutions:x = 3

  18. Example 3 Equation cannot be factorised.

  19. Using quadratic formula We use the substitution A complex number

  20. Equation has 2 complex solutions Real part Imaginary Part

  21. Note: Because the coefficients are real, solutions come in conjugate pairs i.e.

  22. Equation has 2 imaginary solutions.

  23. Forming quadratic equations from 2 solutions. If solutions are

  24. Example 1 Quadratic equation is

  25. Example 2 Quadratic equation is

  26. Example 3

  27. Worksheet 2

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