2.2-2.5 Quadratics and Complex Numbers

Discriminant

100

Find the discriminate and determine the nature of the roots.

x²-7x+10=0

D=9

2 real Rational solutions

200

Find the discriminate and determine the nature of the roots.

x²=8x-7

D=36 

2 Rational real solutions

300

Find the discriminate and determine the nature of the roots.

x-3x²=-3

D=37

2 Real Irrational Roots

400

Find the discriminate and determine the nature of the roots.

3x²-x+2=0

D= -23

 2 imaginary conjugate roots

500

Find the discriminate and determine the nature of the roots.

x(x-10)=-25

D=0, 

1 Real Double Root

Quadratic Formula

100

Solve with the quadratic formula:

x²-10x+25=0

x=5 

200

Solve using the quadratic formula:

2x²-3x=5

x=5/2, -1

300

Solve using the quadratic formula:

3x²+x+2=0

(-1+isqrt23)/6

400

Solve using the quadratic formula: 

x²-4x+5 = 0

2+i, 2-i

500

Solve:

-12=-5x²-8x

(-4 + 2sqrt19)/5

Adding and Subtracting Complex Numbers

100

Simplify:

(4i+3)-(7i+5)

-3i-2

200

Simplify:

(3i+1)-(5i-2)

-2i+3

300

Simplify:

(12-2i)+(2-9i)

14-11i

400

Simplify:

(3x-7yi)+(6x+8yi)

9x+yi

500

Simplify:

(-3-4i)-(-2-8i)

-1+4i

Multiplying Complex Numbers

100

Simplify.

(3i)(4i)

-12

200

Simplify

(5+2i)(1-i)

7-3i

300

Simplify

(4+i)(3+2i)

10+11i

400

Simplify

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

13

500

Simplify.

(4+3i)^2

7+24i

Dividing Complex Numbers

100

Simplify.

4/(3i)

-(4i)/3

200

Simplify:

(3+i)/(5i)

(1-3i)/5

300

Simplify:

4/(2-3i)

(8+12i)/13

400

Simplify.

10/(10 + 5i)

(4-2i)/5

500

Simplify.

(2+6i)/(-3-3i

(-4-2i)/3