Review for TEST #2:

Topics are:

1)Rationalize the denominators.2)Solving quadratic equations, using the quadratic formula.3)Power of i.4)Operations on Complex Numbers.5)Discriniminant 6)Sum and Product of the roots of quadratic equations.

Aim: How do we prepare for TEST #2?

Do Now:

?

Solve: 1) x² – 3x = 9 2) 3x² – 4x + 2 = 0

3) Simplify: :

are

Part I: Rationalize the denominators

Simplify:

Part II: Solving Quadratic Equations, using the Quadratic formula?

Solve: 1) x² + 8x + 25 = 02)4x² – 12x + 25 = 03) x² + 7 = 2x

2 4

2x

cb b a

a

Clock 4 System

1

-1

- i i

Remainder of 0

Remainder of 1

Remainder of 2

Remainder of 3

Part III: Power of i

Part III: Power of i ?

Simplify the following:

1) i8 + i9 + i10 + i11

2) i16 + i6 – 2 i5 + i13

Part IV: Operations on complex numbers?

1 ) Subtract (12 + 3i) from (3 – i), and then graph the result.

Simplify: i

i

i

3

2 3)

3

10)2

4) Find the product of (6 – 2i) and i.

Part V:Discriminant

Value of Discriminant Type and Number of Roots

Example of Graph of Related Function

b2 – 4ac > 0b2 – 4ac is a perfect square.

2 real, rational roots

b2 – 4ac > 0b2 – 4ac is not a perfect square.

2 real, irrational roots

b2 – 4ac = 0 1 real, rational root

b2 – 4ac < 0 2 complex roots

Part V:Discriminant

1) The roots of the equation x² – 7x+ 15 = 0 a) Imaginary b) real, rational, and equalc) real, rational, and unequal d) real, irrational, and unequal

are

2) The roots of the equation 2x² – x = 4

a) Imaginary b) real, rational, and equalc) real, rational, and unequal d) real, irrational

Part VI: Sum and Product of the roots

1) Find the sum and product of roots; 3x² – 2x – 15 = 0

2) Write a quadratic equation whose roots are; a) 6i and – 6i b) 32 and 32

a

cr

a

br

c bx ax²

)roots(r theofProduct , )roots(r theof Sum

:0

2121

Find the second root, r2

#1: If one root of x2 – 6x + k = 0 is 4

#2: If one root of x2 – kx + 18 = 0 is 6