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Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
Oct 21 The Discriminant
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Oct 21 The Discriminant

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  • 1. Question­ If ­3 is one root of x2 + x + c = 0, find the other root                      and the value of c. 1
  • 2. The Discriminant The Nature of Roots b2 ­ 4ac   ­From the quadratic formula is known as the discriminant. ­It allows us to determine if the roots are real or imaginary. ­If the roots are real it also allows us to determine if there are one or two  roots. 2
  • 3. b2 ­ 4ac > 0 There are two roots If   b2 ­ 4ac  is a perfect square the roots are rational If   b2 ­ 4ac  is not a perfect square the roots are  irrational 3
  • 4. b2 ­ 4ac = 0 ­Then there is only one real root ­The function only crosses the x axis at the vertex of the  parabola 4
  • 5. b2 ­ 4ac < 0 ­The roots of the quadratic function are imaginary ­The parabola does not cross the x axis at any point ­There are still imaginary roots to the function 5
  • 6. For each of the following quadratics 1. Find the value of the discriminant. 2. Use the value to determine the nature of the        roots. 3. Use to quadratic formula to find the exact      value for the roots of each quadratic. 4. Draw a very rough sketch of what the quadratic might        look like. a)  x2 ­ x ­12 = 0 b)  ­x2 + 2x + 18 = 0 c)  x2 ­ x + 2 = 0 d)  ­x2 + x ­ 4 = 0 e)  x2 ­ 6x + 9 = 0 f)  ­x2 + 10x ­25 = 0  6
  • 7. a)  x2 ­ x ­12 = 0 7
  • 8. b)  ­x2 + 2x + 18 = 0 8
  • 9. c)  x2 ­ x + 2 = 0 9
  • 10. d)  ­x2 + x ­ 4 = 0 10
  • 11. e)  x2 ­ 6x + 9 = 0 11
  • 12. f)  ­x2 + 10x ­25 = 0  12

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