Algebra 2--Quadratics and Complex Numbers

Discriminant: Number and types of solutions

100

3x^2+5x-2=0

Discriminant 49

2 rational solutions

200

x^2 - 3x + 4 = 0

Discriminant -7

2 imaginary solutions

300

2x^2 - 3x + 4 = 8

Discriminant 41

2 real irrational solutions

400

-4x^2 = 5x + 6

Discriminant -71

2 imaginary solutions

500

−9r^2 − 8r − 1 = r − r^2 − 9

Discriminant 337

2 irrational solutions

Complex Solutions

100

4x^2+9=-80 

isqrt(89)/2, -isqrt(89)/2

200

x^2 - 8x + 40 = 6

4+3i sqrt(2), 4-3i sqrt(2)

300

x^2 + 12x + 64 = -10

-6 + i sqrt(38), -6 - i sqrt(38)

400

11x^2 = -4x - 1

-2/11 + i sqrt(7) / 11, -2/11 - i sqrt(7) / 11

500

6x^2 + 2 = -4x

-1/3 + i sqrt(2) /3 , -1/3 - i sqrt(2) / 3

Powers of i

100

i^0

What is 1

200

i^59

What is 

-i

300

i^12

What is 

1

400

i^34

What is 

-1

500

(i^31)^3

What is 

i

Complex Operations

100

(3+2i)(5-i)

17+7i

200

(1/2i)^3

-1/8i

300

(3+2i)^2

5+12i

400

sqrt(-4)sqrt(-8)

-4sqrt(2)

500

(5+3i)(5-3i)

34

Bring It On!

100

Find g(0). 

g(t) = -16t^2+70t+1

t=1

200

Find the zeros. 

f(x) = x^2-6x+7

3+sqrt(2), 3-sqrt(2)

300

Factor

9x^2-4

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

400

Factor

x^2-3

(x+sqrt(3))(x-sqrt(3))

500

Factor

5x^2+12x-9

(5x-3)(x+3)