Factoring Polynomials & Solving Quadratics by Factoring

Discriminant

100

n² + 8n = -15

4 -- 2 real solutions

200

n² + 3n -12 = 6

-63 -- 2 imaginary solutions

300

n² + 2n + 1 = 0

0 -- 1 real root

400

7k² - 13k + 3 = -3

1 -- 2 real roots

500

9x² + 1=0

-36 -- 2 imaginary roots

Find the Roots

100

n² + 8n = -15

What is x = -5, x = -3

200

x² -11x + 19 = -5

What is x = 8, x = 3

300

n² - 10n + 22 = -2

What is x = 6, x = 4

400

n² + 3n -12 = 6

What is x = 3, x = -6

500

b² + 5b - 35 = 3b

What is x = -7, x = 5

Determine the zeros

100

2n² + 5n + 2 = 0

What is x = -1/2, x = -2

200

3n² -8n + 4 = 0

What is x = 2/3, x = 2

300

6b² - 13b + 3 = -3

What is x = 2/3, x = 3/2

400

7k² - 13k + 3 = -3

(7k-6)(k-1)

500

8x² + 21 = -59x

What is x = -3/8, x = -7

What are the solutions?

100

a² - 9 = 0

What is x = 3, x = -3

200

4m² - 25 = 0

What is x = -5/2, x = 5/2

300

9x² - 1

What is x = 1/3, x = -1/3

400

81x² - 121

What is x = 11/9, x = -11/9

500

1 - r² = 0

What is r = -1, r = 1

Complex Numbers

100

3i(2 + 3i)

-9 + 6i

200

-3i(-5i)

-15

300

(2 + 3i)(2 - 3i)

13

400

(3 + 4i)(3 + 4i)

-7 + 4i

500

5i²(2+i)

-10 - 5i