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## Quadratic Formula - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=1, Mode=easy

Solve using the quadratic formula   x = (-b ± √b2 - 4ac) / 2a,   separating answers with commas. If there is no solution, write "no solution". Sample answers:

4,   3/2
4 + sqrt(4),   4 - sqrt(3)
(1 + 2sqrt(3)) / 2,   (1 - 2sqrt(3)) / 2

 1.   -x 2 + x + 6 = 0 x = 2.   x 2 - 8x + 15 = 0 x =

### Complexity=1, Mode=normal

Solve using the quadratic formula   x = (-b ± √b2 - 4ac) / 2a,   separating answers with commas. If there is no solution, write "no solution". Sample answers:

4,   3/2
4 + sqrt(4),   4 - sqrt(3)
(1 + 2sqrt(3)) / 2,   (1 - 2sqrt(3)) / 2

 1.   - 2x 2 + 3x + 8 = 0 x = 2.   2x 2 + x - 7 = 0 x =

### Complexity=1, Mode=easy

Solve using the quadratic formula   x = (-b ± √b2 - 4ac) / 2a,   separating answers with commas. If there is no solution, write "no solution". Sample answers:

4,   3/2
4 + sqrt(4),   4 - sqrt(3)
(1 + 2sqrt(3)) / 2,   (1 - 2sqrt(3)) / 2

1-x 2 + x + 6 = 0
x =
Solution
Based on ax2 + bx + c, we have:
a = -1, b = 1, c = 6

Plugging into the quadratic formula results in these two answers:

Simplifying...

- 2, 3

2x 2 - 8x + 15 = 0
x =
Solution
Based on ax2 + bx + c, we have:
a = 1, b = -8, c = 15

Plugging into the quadratic formula results in these two answers:

Simplifying...

5, 3

### Complexity=1, Mode=normal

Solve using the quadratic formula   x = (-b ± √b2 - 4ac) / 2a,   separating answers with commas. If there is no solution, write "no solution". Sample answers:

4,   3/2
4 + sqrt(4),   4 - sqrt(3)
(1 + 2sqrt(3)) / 2,   (1 - 2sqrt(3)) / 2

1- 2x 2 + 3x + 8 = 0
x =
Solution
Based on ax2 + bx + c, we have:
a = -2, b = 3, c = 8

Plugging into the quadratic formula results in these two answers:

Simplifying...

 ,

22x 2 + x - 7 = 0
x =
Solution
Based on ax2 + bx + c, we have:
a = 2, b = 1, c = -7

Plugging into the quadratic formula results in these two answers:

Simplifying...

 ,