The quadratic formula, and the discriminant: how many real solutions

Answer Key - Grade 9 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Jun solves x² - 6x + 4 = 0 in pencil. Here a = 1, b = -6 and c = 4. What is b² - 4ac?

   20
2. 2.

   Kira's robot solves 3x² - 4x - 2 = 0. Here a = 3, b = -4 and c = -2. What is b² - 4ac?

   40
3. 3.

   In math club, Luz solves x² + 9x + 14 = 0. Here a = 1, b = 9 and c = 14. What is b² - 4ac?

   25
4. 4.

   Milo's puzzle card shows 5 - 3x + 2x² = 0. Before using the formula, write it in order. What are a, b and c?

   • a = 2, b = -3, c = 0
   • a = 2, b = 3, c = 5
   • a = 2, b = -3, c = 5
   • a = 5, b = -3, c = 2
5. 5.

   Noah copies 4x² + 6 = x from the board. Before using the formula, move every term to the left. What are a, b and c?

   • a = 4, b = 0, c = 6
   • a = 6, b = -1, c = 4
   • a = 4, b = -1, c = 6
   • a = 4, b = 1, c = 6
6. 6.

   Pia's robot reads x² + 9 = 7x. Before using the formula, move every term to the left. What are a, b and c?

   • a = 1, b = 7, c = 9
   • a = 1, b = -7, c = 9
   • a = 9, b = -7, c = 1
   • a = 0, b = -7, c = 9
7. 7.

   Ren's math book shows 3x - x² + 8 = 0. Before using the formula, write it in order. What are a, b and c?

   • a = 1, b = 3, c = 8
   • a = 0, b = 3, c = 8
   • a = 3, b = -1, c = 8
   • a = -1, b = 3, c = 8
8. 8.

   Zee's robot checks 2x² - 3x + 4 = 0. It finds b² - 4ac = 9 - 32 = -23. How many real solutions are there?

   • No real solution
   • Two real solutions
   • One real solution
9. 9.

   Esme checks x² - 8x + 16 = 0 in pencil. It finds b² - 4ac = 64 - 64 = 0. How many real solutions are there?

   • One real solution
   • No real solution
   • Two real solutions
10. 10.

    In math club, Jun checks 9x² + 6x + 1 = 0. It finds b² - 4ac = 36 - 36 = 0. How many real solutions are there?

    • Two real solutions
    • No real solution
    • One real solution