Solving Quadratic Equations

Solve by 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. 2x² - 5x - 3 = 0

x = -1/2 x = 3

Square Roots

100

Solve the following quadratic equation by using square roots: x² = 4

x = 2 x = -2

200

Solve the following quadratic equation by using square roots: x² = 121

+11 or -11

300

Solve the following quadratic equation by using square roots: 4x² = 400

x = 10 x = -10

400

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

1 or -1

500

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

x = 5 x = -5

Factoring

100

Factor the Quadratic Expression:

 x²+15x+36

(x+3)(x+12)

200

Factor the Quadratic Expression:

x²-9

(x+3)(x-3)

300

Factor the quadratic expression:

7x²+63+140

7(x+4)(x+5)

400

Factor the Quadratic Expression:

6x²+7x+1

(6x+1)(x+1)

500

Factor the expression:

5x³+3x²-20x-12

(5x+3)(x-2)(x+2)

Quadratic Formula

100

The Quadratic Formula is used to solve all quadratics in standard form. (what is it?)

What is -b +- sqrt(b² - 4ac) /(2a)?

200

This part of the quadratic formula is used to determine how many real solutions a quadratic has.

What is the discriminant?

(b^2-4ac)

300

Solve the following quadratic equation by using the quadratic formula: x² - 9x + 20 = 0

x = 5 x = 4

400

Solve the following quadratic equation by using the quadratic formula: 2x² + 9x + 4 = 0

x = -1/2 x = -4

500

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

x = 5 x = -3/4

Random

100

Solve.

x²+18 = 9

No Solution

200

Factor.

6x⁵+18x²

6x²(x³+3)

300

Factor Completely.

8x³-50x

2x(2x+5)(2x-5)

400

Factor.

4x²+13x+10

(4x+5)(x+2)

500

Solve.

5x²-2x-10=0

x = 1+- root(51) / 5