ALGEBRA II/TRIG GROUP QUIZ NAME________________________

CHAPTER 10 NAME________________________

NAME________________________

Perform the indicated operations and simplify.

_______________1) i37 2) i-11 3)

_______________ 2)

_______________ 3)

________________4) 5) (2 + 3i) + (1 - 5i) 6) (3 + 9i) – (12 – 5i)

________________5)

________________6)

________________7) (3 + 2i)(4 - 6i) 8) 9) ) Let z = 3 + 4i. Find çz ç.

________________8)

________________9)

_____________________10) Write a quadratic equation with real coefficients if one of the solutions is -5 + 7i.

#11-12. Factor the following polynomials in the complex number system:

________________11) x2 + 6x + 12 12) 16x2 + 121

________________12)

______________________ 13) Solve over the complex number system: 4x2 - 3x + 8 = 0

______________________14) Plot the graph with the given domain and find all the zeros

f(x) = x3 + 3x2 - 13x - 15 -6 ≤ x ≤ 1

*You will need to scale the y-axis*

_________________15) Use synthetic substitution to find P(-3) in P(x) = x3 - 3x2 - x + 3

#16-19. Use P(x) = x3 - 2x2 - 2x + 12

16) Use Descartes’ Rule of Signs to find the possible number of positive, negative, and non-real zeros, using

The chart below.

Reals

+ - non-real

_____________ 17) Find the least integer that is

an upper bound.

_____________ 18) Find the greatest integer that

is a lower bound.

__________________ 19) Find all the zeros.

20) Airplane Payload problem. The payload an airplane will carry is a cubic function of the length of the plane. Suppose that for a particular design of plane the equation is:

P(L) = -L3 + 6L2 - 2L – 3

Where P(L) is the number of tons of payload, and L is the length of the plane in tens of meters.

a) Evaluate and graph P(L) in the domain -1≤ L≤ 6

________________ b) P(L) has an integer zero. What is it?

________________ c) Find all the zeros. (Round to the nearest tenth, do not leave in radical form!)

d) An airplane will fly only if the payload it can carry is positive. Shade the portion of your graph that

represents planes that will fly.

________________ e) Approximately how long is the longest plane that will fly?