Quadratic equations with complex solutions

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Ren's robot reads 2x² − 4x + 5 = 0: a = 2, b = -4, c = 5. What is b² − 4ac?

   -24
2. 2.

   Tala works on x² + 2x + 26 = 0, where a = 1, b = 2 and c = 26. What is b² − 4ac?

   -100
3. 3.

   Zee solves x² + 36 = 0 on a puzzle card. Which shows all the solutions?

   • No solution
   • x = 6i
   • x = 6 or x = -6, with the i dropped
   • x = 6i or x = -6i
4. 4.

   Esme writes x² = -64 on the board. Which shows all the solutions?

   • x = 8i
   • x = 8 or x = -8, with the i left off
   • x = 8i or x = -8i
   • No solution
5. 5.

   Jun's robot solves 3x² + 75 = 0. Which shows all the solutions?

   • x = 5i
   • x = 5 or x = -5, with no i written
   • x = 5i or x = -5i
   • No solution
6. 6.

   Kira solves x² + 121 = 0 for a math club puzzle. Which shows all the solutions?

   • x = 11i or x = -11i
   • x = 11i
   • No solution
   • x = 11 or x = -11
7. 7.

   Luz uses the formula on x² + 2x + 10 = 0. Here b² − 4ac = 4 − 40 = -36. What is √(-36), written with i?

   6i
8. 8.

   Milo solves x² − 4x + 8 = 0. Here b² − 4ac = 16 − 32 = -16. What is √(-16), written with i?

   4i
9. 9.

   Noah's robot gets b² − 4ac = 36 − 100 = -64 for x² + 6x + 25 = 0. What is √(-64), written with i?

   8i
10. 10.

    Pia finds b² − 4ac = 4 − 200 = -196 for x² − 2x + 50 = 0. What is √(-196), written with i?

    14i