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

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Milo wants exact answers for x² - 4x - 1 = 0. Which gives both exact solutions?

   • x = 2 ± 2√5
   • x = 2 ± √5
   • x = 2 ± √3
   • x = -2 ± √5
2. 2.

   Noah's robot gives exact answers only. It solves x² + 6x + 2 = 0. Which gives both exact solutions?

   • x = -3 ± √11
   • x = -3 ± √7
   • x = -3 ± 2√7
   • x = 3 ± √7
3. 3.

   Pia solves x² - 2x - 11 = 0 exactly, root sign and all. Which gives both exact solutions?

   • x = 1 ± 2√3
   • x = -1 ± 2√3
   • x = 1 ± 4√3
   • No real solution
4. 4.

   In math club, Ren finds the exact solutions of x² + 8x + 13 = 0. Which gives both exact solutions?

   • x = 4 ± √3
   • x = -4 ± 2√3
   • x = -4 ± √29
   • x = -4 ± √3
5. 5.

   Zee's robot picks c so that x² - 8x + c = 0 has exactly one solution. What is c?

   16
6. 6.

   Esme needs 2x² + 12x + c = 0 to touch the x-axis at one point only. What is c?

   18
7. 7.

   Kira solves x² = 4x + 3 with the formula. What is the positive solution, to the nearest tenth?

   4.6
8. 8.

   Luz's robot solves 3x² + 1 = 6x. What is the larger solution, to the nearest tenth?

   1.8
9. 9.

   Milo solves 2x² = 7 - 3x in pencil. What is the positive solution, to the nearest tenth?

   1.3
10. 10.

    In math club, Noah solves x(x + 5) = 3. What is the smaller solution, to the nearest tenth?

    -5.5