Name:  ___________________________________             Worksheet –Solving Quadratic Equations.

 

RULES:

1.      FACTOR out any common monomial. 

:    Note: If equation is not equal to zero use additive inverse to get = 0.

2.      If the coefficient of x^2 is 1 or the constant is 1, write a list of the pairs of FACTORs for number. 

3.      Look at the middle term coefficient and see which 2 factors add to that number.

:    Note:  If no middle term with a degree of one, see if the x^2 term and constant are perfect squares.

4.      Use those numbers in the binomial written in the form (         ) (        ).  Check using FOIL.

5.      Set each term equal to zero.

6.      Solve for X.

7.      Record answers in set form.

8.      Check in the original quadratic function with value one

9.      Check in the original quadratic function with value two (if there are two answers)

 

EXAMPLE:   x^2 + 3x – 18 = 0

1.      No common monomial

2.      {-1, 18}, {1, -18}, {2, -9}, {-2, 9}, {3, -6}, {-3, 6}

3.      -3 + 6 = 3

4.      (x – 3) (x + 6) = 0

5.      x – 3 = 0, x + 6 = 0

6.      x = 3, x = -6

7.      {-6, 3}

8.      check x = -6:  (-6)^2 + 3(-6) – 18 = 0;  36 – 18 – 18 = 0;  0 = 0

9.      check x = 3:   (3)^2 + 3(3) – 18 = 0;  9 + 9 – 18 = 0;  0 = 0

 

EXAMPLE:   2x^3 – 12 x^2 + 18x = 0

1.      2x (x^2 – 6x + 9)

2.      {3, 3}, {-3, -3}, {1, 9}, {-1, -9}

3.      -3 + -3 = -6

4.      2x (x -3) (x -3) = 0

5.      2x = 0, (x – 3) = 0

6.      x = 0, x = 3

7.      {0, 3)

8.      check x = 0: so 0 = 0 (common sense) 

9.      check x = 3: 2(3)^3 – 12 (3)^2 + 18(3) = 0; 54 – 108 + 54 = 0;  0 = 0

 

NOW YOU FOLLOW THE PROCESS:   Show work on notebook paper!

 

1.      x^2 + 4x + 4 = 0

2.      x^2 – 6x + 8 = 0

3.      x^2 – 5x – 6 = 0

4.      4a^2 – 25 = 0

5.      m^2 – 4m  = 3

6.      x^2 + 3x – 5 = 0

7.      x^3 + 7x^2 + 12x = 0

8.      12x^2 – 48 = 0

9.      x^2 + 6x – 10 = 0

10.  x^3 + x^2 – 30x = 0