Math Practice Problems - Quadratic Zero Equations

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. Write answers in ascending order, separated by commas. Example: x=-3/2,2

1. x² + x - 6 = 0
x =

2. x² + 2x + 1 = 0
x =

Complexity=3, Mode=prefix

Factor the expression and solve for the zeros. Write answers in ascending order, separated by commas. Example: x=-3/2,2

1. 8x² - 64x + 56 = 0
x =

2. x² - 6x + 9 = 0
x =

Complexity=3, Mode=frontConst

Factor the expression and solve for the zeros. Write answers in ascending order, separated by commas. Example: x=-3/2,2

1. ^-4x³ + 46x² - 120x = 0
x =

2. x³ + 6x² - 16x = 0
x =

Complexity=4, Mode=frontConst

Factor the expression and solve for the zeros. Write answers in ascending order, separated by commas. Example: x=-3/2,2

1. ^-12x³ - 45x² - 27x = 0
x =

2. 3x³ - 9x² - 12x = 0
x =

Answers

Complexity=1, Mode=simple

Factor the expression and solve for the zeros. Write answers in ascending order, separated by commas. Example: x=-3/2,2

Problem

Correct Answer

Your Answer

x² + x - 6 = 0

x =

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

Now solve each fragment for 0

x + 3 = 0
x = -3

x - 2 = 0
x = 2

Problem

Correct Answer

Your Answer

x² + 2x + 1 = 0

x =

Solution
Factor to get ( x + 1)² = 0

Now solve each fragment for 0

x + 1 = 0
x = -1

Complexity=3, Mode=prefix

Factor the expression and solve for the zeros. Write answers in ascending order, separated by commas. Example: x=-3/2,2

Problem

Correct Answer

Your Answer

8x² - 64x + 56 = 0

x =

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

Now solve each fragment for 0

x - 1 = 0
x = 1

x - 7 = 0
x = 7

Problem

Correct Answer

Your Answer

x² - 6x + 9 = 0

x =

Solution
Factor to get ( x - 3)² = 0

Now solve each fragment for 0

x - 3 = 0
x = 3

Complexity=3, Mode=frontConst

Factor the expression and solve for the zeros. Write answers in ascending order, separated by commas. Example: x=-3/2,2

Problem

Correct Answer

Your Answer

^-4x³ + 46x² - 120x = 0

x =

Solution
Factor to get ^-2x(x - 4)(2x - 15) = 0

Now solve each fragment for 0

^-2x = 0
x = 0

x - 4 = 0
x = 4

2x - 15 = 0
x = 15/2

Problem

Correct Answer

Your Answer

x³ + 6x² - 16x = 0

x =

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

Now solve each fragment for 0

x = 0
x = 0

x + 8 = 0
x = -8

x - 2 = 0
x = 2

Complexity=4, Mode=frontConst

Factor the expression and solve for the zeros. Write answers in ascending order, separated by commas. Example: x=-3/2,2

Problem

Correct Answer

Your Answer

^-12x³ - 45x² - 27x = 0

x =

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

Now solve each fragment for 0

^-3x = 0
x = 0

x + 3 = 0
x = -3

4x + 3 = 0
x = -3/4

Problem

Correct Answer

Your Answer

3x³ - 9x² - 12x = 0

x =

Solution
Factor to get 3x(x + 1)(x - 4) = 0

Now solve each fragment for 0

3x = 0
x = 0

x + 1 = 0
x = -1

x - 4 = 0
x = 4

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