#2

• Discriminant


  Used to determine the nature of the roots
• Nature of the roots if the discriminant is negative


  • Imaginary or no real root
  • Real, irrational and unequal
  • Real, rational and equal
  • Real, rational and unequal
• Discriminant of a quadratic equation


  b² - 4ac
• Discriminant values that characterize the real, rational and equal roots of a quadratic equation

  • -4
  • 0
  • 4
  • 10
• Sum of the roots of ax² + bx + c = 0

  • b/a
• The product of the roots of a quadratic equation is (c/a)
• Determining the quadratic equation given its roots

  x² + (r1 + r2)x + (r1)(r2) = 0
• The roots of a quadratic equation are 2 and 3, and the product of the roots is 6. The sum of the roots is 5.
• The roots of the quadratic equation 3x² + 5x - 70 = 0 are -8 and 7.
• The quadratic equation with roots 3 and -4 is x² - x - 12 = 0.
• Standard form of a quadratic equation


  ax² + bx + c = 0
• The quadratic equation x(x-2)+5=0 has standard form x² + 2x - 5 = 0, with sum of roots -2 and product of roots -5.
• The quadratic equation with roots -4 and -1 is x² + 5x + 4 = 0.
• The quadratic equation with roots 1/3 and 1/2 is 6x² - 7x + 2 = 0.
• Transforming (x-1)² + (x-2)² - 13 = 0 into standard form

  1. Identify the common monomial factor

  2. Use distributive property

  3. Use factoring method

  4. Use foil method in simplifying expression
• The standard form of the equation (x-1)² + (x-2)² - 13 = 0 is 2x² - 6x - 8 = 0.
• The roots of the quadratic equation (x-1)² + (x-2)² - 13 = 0 are 4 and -1.