Answer to Matched Exercise

Detailed solution and answer to the matched exercise in Solve Quadratic Equations Using Discriminants (2) are presented.




Matched Exercise 1: Find all values of the parameter m in the quadratic equation


x 2 + x + m + 1 = 0
such that the equation has
  1. one solution,
  2. 2 real solutions, and
  3. 2 complex solutions.

Solution to Matched Exercise 1:

  • Given
    x 2 + x + m + 1 = 0

  • Find the discriminant>
    D = b2 - 4ac = 12 - 4(1)(m + 1) = -3 - 4m

  • For the equation to have one solution, the discriminant has to be equal to zero.
    -3 - 4m = 0

  • Solve the above equation for m.
    m = -3/4

  • For the equation to have 2 real solution, the discriminant has to be greater than zero.
    -3 - 4m > 0

  • The inequality -3 - 4m > 0 has the following solution set.
    (-infinity , -3/4)

  • For the equation to have 2 complex solution, the discriminant has to be less than zero.
    -3 - 4m < 0

  • The inequality -3 - 4m > 0 has the following solution set.
    (-3/4, +infinity)

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