Answer to Matched Exercise on Quadratic Equations (2)

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.
    (-∞ , - 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 , + ∞)

More References and links

Solve Equations, Systems of Equations and Inequalities.