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## Quadratic Zero Equations - 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=simple

Factor the expression and solve for the zeros. Separate answers with commas. Example: x=-3/2,2

 1.   x 2 + 8x + 7 = 0 x = 2.   x 2 + 8x - 20 = 0 x =

### Complexity=3, Mode=prefix

Factor the expression and solve for the zeros. Separate answers with commas. Example: x=-3/2,2

 1.   - 3x 3 - 9x 2 + 84x = 0 x = 2.   x 3 - 19x 2 + 34x = 0 x =

### Complexity=3, Mode=frontConst

Factor the expression and solve for the zeros. Separate answers with commas. Example: x=-3/2,2

 1.   2x 2 - 5x - 25 = 0 x = 2.   - 4x 2 - 2x + 12 = 0 x =

### Complexity=4, Mode=frontConst

Factor the expression and solve for the zeros. Separate answers with commas. Example: x=-3/2,2

 1.   4x 3 + 16x 2 - 33x = 0 x = 2.   6x 3 - 46x 2 + 68x = 0 x =

### Complexity=1, Mode=simple

Factor the expression and solve for the zeros. Separate answers with commas. Example: x=-3/2,2

1x 2 + 8x + 7 = 0
x =
Solution
Factor to get (x + 1)(x + 7) = 0

Now solve each fragment for 0

x + 1 = 0
x = -1

x + 7 = 0
x = -7

2x 2 + 8x - 20 = 0
x =
Solution
Factor to get (x + 10)(x - 2) = 0

Now solve each fragment for 0

x + 10 = 0
x = -10

x - 2 = 0
x = 2

### Complexity=3, Mode=prefix

Factor the expression and solve for the zeros. Separate answers with commas. Example: x=-3/2,2

1- 3x 3 - 9x 2 + 84x = 0
x =
Solution
Factor to get - 3x(x + 7)(x - 4) = 0

Now solve each fragment for 0

- 3x = 0
x = 0

x + 7 = 0
x = -7

x - 4 = 0
x = 4

2x 3 - 19x 2 + 34x = 0
x =
Solution
Factor to get x(x - 2)(x - 17) = 0

Now solve each fragment for 0

x = 0
x = 0

x - 2 = 0
x = 2

x - 17 = 0
x = 17

### Complexity=3, Mode=frontConst

Factor the expression and solve for the zeros. Separate answers with commas. Example: x=-3/2,2

12x 2 - 5x - 25 = 0
x =
Solution
Factor to get (x - 5)(2x + 5) = 0

Now solve each fragment for 0

x - 5 = 0
x = 5

2x + 5 = 0
x = -5/2

2- 4x 2 - 2x + 12 = 0
x =
Solution
Factor to get - 2(x + 2)(2x - 3) = 0

Now solve each fragment for 0

x + 2 = 0
x = -2

2x - 3 = 0
x = 3/2

### Complexity=4, Mode=frontConst

Factor the expression and solve for the zeros. Separate answers with commas. Example: x=-3/2,2

14x 3 + 16x 2 - 33x = 0
x =
Solution
Factor to get x(2x + 11)(2x - 3) = 0

Now solve each fragment for 0

x = 0
x = 0

2x + 11 = 0
x = -11/2

2x - 3 = 0
x = 3/2

26x 3 - 46x 2 + 68x = 0
x =
Solution
Factor to get 2x(x - 2)(3x - 17) = 0

Now solve each fragment for 0

2x = 0
x = 0

x - 2 = 0
x = 2

3x - 17 = 0
x = 17/3