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Quadratic Equations Practice Problems

based on 15 ratings
By — McGraw-Hill Professional
Updated on Sep 27, 2011

Quadratic Equations Practice Problems

Set 1: Solving Quadratic Equations - When the Product of Two Numbers is Zero

To review quadratic equations, go to Quadratic Equations Help

Practice

  1. x 2x – 12 = 0
  2. x 2 + 7 x + 12 = 0
  3. x 2 + 8 x = –15
  4. x 2 – 10 x = – 21
  5. 3 x 2x – 2 = 0
  6. 4 x 2 – 8 x = 5
  7. x 2 – 25 = 0
  8. 9 x 2 – 16 = 0
  9. x 2 = 100
  10. x 2 + 6 x + 9 = 0
  11. x 2 = 0
  12. 5 x 2 = 0

Double Inequalities Examples

Solutions

  1. x 2x – 12 = 0

    ( x4 )( x + 3)= 0

    Double Inequalities Examples

  2. x 2 + 7 x + 12 = 0

    ( x + 3)( x + 4)= 0

    Double Inequalities Examples

  3. x 2 + 8 x = – 15

    +15 + 15

    x 2 + 8 x + 15 = 0

    ( x + 3)( x + 5)= 0

    Double Inequalities Examples

  4. x 2 – 10 x = – 21

    +21 + 21

    x 2 – 10 x + 21 = 0

    ( x – 3)( x – 7)= 0

    Double Inequalities Examples

  5. 3 x 2x – 2 = 0

    (3 x + 2)( x –1)= 0

    Double Inequalities Examples

  6. 4 x 2 – 8 x = 5

    – 5 – 5

    4 x 2 – 8 x –5 = 0

    (2 x + 1)(2 x – 5)= 0

    Double Inequalities Examples

  7. x 2 – 25 = 0

     ( x – 5)( x + 5) = 0

    Double Inequalities Examples

Double Inequalities Examples

Double Inequalities Examples

  1. x 2 + 6 x + 9 = 0

    ( x + 3)( x + 3)= 0

    x + 3 = 0

    – 3 – 3

    x = – 3

  2. x 2 = 0

    ( x )( x )= 0

    x = 0

  3. 5 x 2 = 0

    5( x )( x )= 0

    x = 0

Double Inequalities Examples

Set 2: Solving Quadratic Equations - Multiplying and Dividing Both Sides of the Equation

To review dealing with quadratic expressions that are not so easy to factor, go to Quadratic Equations Help

Practice

1. – x 2x + 30 = 0

2. –9 x 2 + 25 = 0

3. 0.01 x 2 + 0.14 x + 0.13 = 0

4. –0.1 x 2 + 1.1 x – 2.8 = 0

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

9. 6 x 2 + 18 x – 24 = 0

10. –10 x 2 – 34 x – 12 = 0

Solutions

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD).

Set 3: Solving Quadratic Equations - Simplifying Squares and Roots

Sometimes using the fact that x 2 = k implies Double Inequalities Clear the fraction by multiplying both sides of the equation by 4 (the LCD). can be used to solve quadratic equations.

To review this concept, go to Quadratic Equations Help

Practice

  1. x 2 – 81 = 0
  2. 64 – x 2 = 0
  3. 4 x 2 = 100
  4. 2 x 2 = 3
  5. – 6 x 2 = – 80

Solutions

  1. x 2 – 81 = 0

    x 2 = 81

    x = ±9

  2. 64 – x 2 = 0

    64 = x 2

    ±8 = x

Double Inequalities

Double Inequalities

Double Inequalities

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