Quadratic Equations Quiz

Grade 9 · Math · Quiz

Test your mastery of solving quadratic equations by factoring, square roots, and the quadratic formula.

Questions

1. Solve by factoring: x² − 7x + 12 = 0

   1. x = 3 or x = 4
   2. x = −3 or x = −4
   3. x = 2 or x = 6
   4. x = 1 or x = 12
   Show answer

   Answer: x = 3 or x = 4

   Factor: (x − 3)(x − 4) = 0 → x = 3 or x = 4.

2. The equation x² + 4 = 0 has two real solutions.

   Show answer

   Answer: False

   x² = −4 has no real solutions since squares cannot be negative.

3. What is the discriminant of x² − 6x + 9 = 0?

   1. 36
   2. 0
   3. −36
   4. 9
   Show answer

   Answer: 0

   b² − 4ac = 36 − 4(1)(9) = 36 − 36 = 0.

4. Solve: x² = 144. The positive solution is x = ___.

   Show answer

   Answer: 12

   √144 = 12.

5. Solve using the quadratic formula: x² + 2x − 8 = 0

   1. x = 2 or x = −4
   2. x = 4 or x = −2
   3. x = −2 or x = 4
   4. x = 2 or x = 4
   Show answer

   Answer: x = 2 or x = −4

   Discriminant = 4 + 32 = 36; x = (−2 ± 6)/2 = 2 or −4.

6. If the discriminant equals zero, the quadratic has exactly one repeated solution.

   Show answer

   Answer: True

   Discriminant = 0 means one repeated root: x = −b/2a.

7. Which is a solution to x² − 9 = 0?

   1. x = 3 only
   2. x = −3 only
   3. x = ±3
   4. x = ±9
   Show answer

   Answer: x = ±3

   x² = 9 → x = ±√9 = ±3.

8. In the quadratic formula, the expression b² − 4ac is called the ___.

   Show answer

   Answer: discriminant

   The discriminant b² − 4ac determines the number and nature of roots.

9. Solve: 2x² − 8 = 0

   1. x = ±1
   2. x = ±2
   3. x = ±4
   4. x = ±8
   Show answer

   Answer: x = ±2

   2x² = 8 → x² = 4 → x = ±2.

10. How many real solutions does x² + 2x + 5 = 0 have? (discriminant = −16)

    1. Zero
    2. One
    3. Two
    4. Four
    Show answer

    Answer: Zero

    A negative discriminant means no real solutions exist.

Get a personalized course on Quadratic Equations built around your child.