Solving Quadratic Equations

Factoring

100

Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0

x = 7 x = -2

200

Solve the following quadratic equation by factoring. x²+3x+2 = 0

x = -2 x = -1

300

Solve the following quadratic equation by factoring. x² - 6x + 5 = 0

x = 5 x = 1

400

Solve the following quadratic equation by factoring. x² - 6x - 27 = 0

x = 9 x = -3

500

Solve the following quadratic equation by factoring. 5x² - 58x - 24 = 0

x = -2/5 x = 12

Square Roots

100

Solve the following quadratic equation by using square roots: 

x² = 48

x =

 4sqrt3 

 = -

 -4sqrt3 

200

Solve the following quadratic equation by using square roots: x² -9 = -8

1 or -1

300

Solve the following quadratic equation by using square roots: 5x² + 3 = 128

x = 5 x = -5

400

Solve the following quadratic equation by using square roots: (4x+1)(x - 3) = 9x - 28

x = 5/2

500

Dalia said she can solve this by using the square root method.  Is she correct, explain/prove your answer.

(5x - 2)² = (2x+ 1)²

No, this does not yield the full answer, rather only one of the roots.  To use the square root method you isolate the squared term and set it equal to a constant; there can't be an x term in the equation.

Completing the Square

100

Solve the following quadratic equation by completing the square: x² + 6x = -8

x = -2 x = -4

200

Solve the following quadratic equation by completing the square: x² - 6x = -5

x = 1 x = 5

300

Solve the following quadratic equation by completing the square: x² - 2x - 24 = 0

x = -4 x = 6

400

Solve the following quadratic equation by completing the square: x² + 10x +16 = 0

x = -2 x = -8

500

Solve the following quadratic equation by completing the square: 2x² - 8x = 10

x = 5 x = -1

Quadratic Formula

100

What is the quadratic formula?

x = -b +- sqrt(b² - 4ac) /(2a)

200

Solve the following quadratic equation by using the quadratic formula: x² + 6x + 5 = 0

x = -1 x = -5

300

Solve the following quadratic equation by using the quadratic formula: 3x² - 5x - 1 = 0

x = (5+sqrt(37))/6

x = (5-sqrt(37))/6

400

Solve the following quadratic equation by using the quadratic formula: (2x+3)(2x + 9) = 2(2x+1)

x = -5/2

500

Solve the following quadratic equation by using the quadratic formula: 4x² - 17x - 15 = 0

x = 5 x = -3/4

Word Problems

100

Find the quadratic equation that is used to solve this problem and state the answer: two consecutive positive odd integers if the sum of their squares is 514.

x² + (x+1)² = 514

{15, 17}

200

Find the quadratic equation that is used to solve this problem and state the answer: two consecutive odd integers if the difference between their squares is 16.

x² - (x+2)² = 16 and the roots are negative or positive {3,5}

300

Find the quadratic equation that is used to solve this problem and state the answer: Find three consecutive even integers if the sum of their squares is 1208.

x²+(x+2)²+(x+4)²=1208

negative and positive {18, 20, 22}

400

Find the quadratic equation that is used to solve this problem and state the answer: Three brothers have ages that are consecutive even integers. The product of the first and third boys’ ages is 20 more than twice the second boys age. Find the age of each of the three boys.

x(x+4) = 20 + 2(x+2) and the brothers are 4, 6, and 8 years old.

500

Find the quadratic equation that is used to solve this problem and state the answer: If one side of a square is increased by one and another is the other side is increased by two, a rectangle is formed with an area of 2 less than twice the area of the square. Find the length of a side of the square.

(x+2)(x+1) = 2x² - 2 and the length of the side of the square is 4.