Quadratic equations with complex solutions

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Zee checks whether 2 − 5i solves x² − 4x + 29 = 0. What is (2 − 5i)² − 4(2 − 5i) + 29?

   0
2. 2.

   Esme checks whether 1 + 2i solves x² − 2x + 7 = 0. What is (1 + 2i)² − 2(1 + 2i) + 7?

   2
3. 3.

   Jun checks whether -1 + i solves x² + 2x + 5 = 0. What is (-1 + i)² + 2(-1 + i) + 5?

   3
4. 4.

   Luz builds a puzzle whose solutions are 3 + 2i and 3 − 2i. Type x² as x^2. Which x² + bx + c has these solutions?

   x^2 − 6x + 13
5. 5.

   Milo builds a puzzle whose solutions are -2 + 5i and -2 − 5i. Type x² as x^2. Which x² + bx + c has these solutions?

   x^2 + 4x + 29
6. 6.

   Noah builds a puzzle whose solutions are 4 + i and 4 − i. Type x² as x^2. Which x² + bx + c has these solutions?

   x^2 − 8x + 17
7. 7.

   Pia builds a puzzle whose solutions are -5 + 2i and -5 − 2i. Type x² as x^2. Which x² + bx + c has these solutions?

   x^2 + 10x + 29
8. 8.

   Ren solves x² + 20 = 4x for a math club puzzle. Which shows both solutions?

   • x = 2 ± 2√6
   • x = 2 ± 8i
   • x = -2 ± 4i
   • x = 2 ± 4i
9. 9.

   Zee's robot solves x² + 34 = 6x. Which shows both solutions?

   • x = -3 ± 5i
   • x = 3 ± 5i
   • x = 3 ± 10i
   • x = 3 ± √43
10. 10.

    Esme solves x² + 13 = -4x on the board. Which shows both solutions?

    • x = 2 ± 3i
    • x = -2 ± √17
    • x = -2 ± 3i
    • x = -2 ± 6i