Use the coefficients and the discriminant part of the quadratic formula (b2 − 4ac) to find the value of each discriminant. Then predict the nature and number of solutions for each equation:

  1. 3x2 – 4x – 2 = 0
    Interactive popup. Assistance may be required.

    Check Your Answer

    D = (-4)2 – 4(3)(-2) = 16 – (-24) = 40
    Two real, irrational, roots. Close Pop Up
  2. x2 + 2x + 8 - 0

    Interactive popup. Assistance may be required.

    Check Your Answer

    D = 22 – 4(1)(8) = 4 – 32 = -28
    Two imaginary (complex) roots. Close Pop Up
  3. x2 + 6x + 9 = 0

    Interactive popup. Assistance may be required.

    Check Your Answer

    D = 62 – 4(1)(9) = 36 – 36 = 0
    One real, rational, root. Close Pop Up
  4. x2 – 8x + 7 = 0

    Interactive popup. Assistance may be required.

    Check Your Answer

    Answer: D = (-8)2 – 4(1)(7) = 64 – 28 = 36
    Two real, rational, roots. Close Pop Up
  5. In your notes, describe in your own words the x-intercepts on the graphs of the quadratic equations with the different types of discriminants (D).

    Interactive popup. Assistance may be required.

    Check Your Answer

    Possible answer:
    D = positive number: two x-intercepts
    D =0: one x-intercept
    D =negative number: no x-intercepts Close Pop Up
  6. For further practice, go to: The Discriminant in Quadratic Equations . Scroll down the page just past Example 1 to the practice problems.