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

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Kira solves 2x² + 7x - 15 = 0 with the quadratic formula. What is the larger solution?

   3/2
2. 2.

   Luz's robot uses the formula on 2x² - 13x - 15 = 0. What is the larger solution?

   15/2
3. 3.

   Milo solves 3x² - 13x - 10 = 0 with the formula, step by step. What is the smaller solution?

   -2/3
4. 4.

   In math club, Noah uses the formula on 5x² - 6x - 8 = 0. What is the smaller solution?

   -4/5
5. 5.

   Pia checks 2x² + 3x + 5 = 0 before solving. How many real solutions does it have?

   • Two real solutions
   • No real solution
   • One real solution
6. 6.

   Ren's robot checks x² - 10x + 25 = 0. How many real solutions does it have?

   • No real solution
   • Two real solutions
   • One real solution
7. 7.

   Tala checks 3x² - 5x - 4 = 0 in pencil. How many real solutions does it have?

   • Two real solutions
   • One real solution
   • No real solution
8. 8.

   In math club, Zee checks 4x² + 4x + 1 = 0. How many real solutions does it have?

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

   Kira solves 3x² + 2x - 4 = 0 in pencil. What is the negative solution, to the nearest tenth?

   -1.5
10. 10.

    In math club, Luz solves x² - 8x + 5 = 0. What is the smaller solution, to the nearest tenth?

    0.7