 3.4.1: Fill in the blanks. The ________ ________ of ________ states that i...
 3.4.2: Fill in the blanks. The ________ ________ ________ states that if i...
 3.4.3: Fill in the blanks. The test that gives a list of the possible rati...
 3.4.4: Fill in the blanks. If is a complex zero of a polynomial with real ...
 3.4.5: Fill in the blanks. Every polynomial of degree with real coefficien...
 3.4.6: Fill in the blanks. A quadratic factor that cannot be factored furt...
 3.4.7: Fill in the blanks. The theorem that can be used to determine the p...
 3.4.8: Fill in the blanks. A real number is a(n) ________ bound for the re...
 3.4.9: In Exercises 914, find all the zeros of the function
 3.4.10: In Exercises 914, find all the zeros of the function
 3.4.11: In Exercises 914, find all the zeros of the function
 3.4.12: In Exercises 914, find all the zeros of the function
 3.4.13: In Exercises 914, find all the zeros of the function
 3.4.14: In Exercises 914, find all the zeros of the function
 3.4.15: In Exercises 1518, use the Rational Zero Test to list all possible ...
 3.4.16: In Exercises 1518, use the Rational Zero Test to list all possible ...
 3.4.17: In Exercises 1518, use the Rational Zero Test to list all possible ...
 3.4.18: In Exercises 1518, use the Rational Zero Test to list all possible ...
 3.4.19: In Exercises 1928, find all the rational zeros of the function
 3.4.20: In Exercises 1928, find all the rational zeros of the function
 3.4.21: In Exercises 1928, find all the rational zeros of the function
 3.4.22: In Exercises 1928, find all the rational zeros of the function
 3.4.23: In Exercises 1928, find all the rational zeros of the function
 3.4.24: In Exercises 1928, find all the rational zeros of the function
 3.4.25: In Exercises 1928, find all the rational zeros of the function
 3.4.26: In Exercises 1928, find all the rational zeros of the function
 3.4.27: In Exercises 1928, find all the rational zeros of the function
 3.4.28: In Exercises 1928, find all the rational zeros of the function
 3.4.29: In Exercises 2932, find all real solutions of the polynomial equation.
 3.4.30: In Exercises 2932, find all real solutions of the polynomial equation.
 3.4.31: In Exercises 2932, find all real solutions of the polynomial equation.
 3.4.32: In Exercises 2932, find all real solutions of the polynomial equation.
 3.4.33: In Exercises 3336, (a) list the possible rational zeros of (b) sket...
 3.4.34: In Exercises 3336, (a) list the possible rational zeros of (b) sket...
 3.4.35: In Exercises 3336, (a) list the possible rational zeros of (b) sket...
 3.4.36: In Exercises 3336, (a) list the possible rational zeros of (b) sket...
 3.4.37: In Exercises 37 40, (a) list the possible rational zeros of (b) use...
 3.4.38: In Exercises 37 40, (a) list the possible rational zeros of (b) use...
 3.4.39: In Exercises 37 40, (a) list the possible rational zeros of (b) use...
 3.4.40: In Exercises 37 40, (a) list the possible rational zeros of (b) use...
 3.4.41: GRAPHICAL ANALYSIS In Exercises 41 44, (a) use the zero or root fea...
 3.4.42: GRAPHICAL ANALYSIS In Exercises 41 44, (a) use the zero or root fea...
 3.4.43: GRAPHICAL ANALYSIS In Exercises 41 44, (a) use the zero or root fea...
 3.4.44: GRAPHICAL ANALYSIS In Exercises 41 44, (a) use the zero or root fea...
 3.4.45: In Exercises 4550, find a polynomial function with real coefficient...
 3.4.46: In Exercises 4550, find a polynomial function with real coefficient...
 3.4.47: In Exercises 4550, find a polynomial function with real coefficient...
 3.4.48: In Exercises 4550, find a polynomial function with real coefficient...
 3.4.49: In Exercises 4550, find a polynomial function with real coefficient...
 3.4.50: In Exercises 4550, find a polynomial function with real coefficient...
 3.4.51: In Exercises 5154, write the polynomial (a) as the product of facto...
 3.4.52: In Exercises 5154, write the polynomial (a) as the product of facto...
 3.4.53: In Exercises 5154, write the polynomial (a) as the product of facto...
 3.4.54: In Exercises 5154, write the polynomial (a) as the product of facto...
 3.4.55: In Exercises 55 62, use the given zero to find all the zeros of the...
 3.4.56: In Exercises 55 62, use the given zero to find all the zeros of the...
 3.4.57: In Exercises 55 62, use the given zero to find all the zeros of the...
 3.4.58: In Exercises 55 62, use the given zero to find all the zeros of the...
 3.4.59: In Exercises 55 62, use the given zero to find all the zeros of the...
 3.4.60: In Exercises 55 62, use the given zero to find all the zeros of the...
 3.4.61: In Exercises 55 62, use the given zero to find all the zeros of the...
 3.4.62: In Exercises 55 62, use the given zero to find all the zeros of the...
 3.4.63: In Exercises 6380, find all the zeros of the function and write the...
 3.4.64: In Exercises 6380, find all the zeros of the function and write the...
 3.4.65: In Exercises 6380, find all the zeros of the function and write the...
 3.4.66: In Exercises 6380, find all the zeros of the function and write the...
 3.4.67: In Exercises 6380, find all the zeros of the function and write the...
 3.4.68: In Exercises 6380, find all the zeros of the function and write the...
 3.4.69: In Exercises 6380, find all the zeros of the function and write the...
 3.4.70: In Exercises 6380, find all the zeros of the function and write the...
 3.4.71: In Exercises 6380, find all the zeros of the function and write the...
 3.4.72: In Exercises 6380, find all the zeros of the function and write the...
 3.4.73: In Exercises 6380, find all the zeros of the function and write the...
 3.4.74: In Exercises 6380, find all the zeros of the function and write the...
 3.4.75: In Exercises 6380, find all the zeros of the function and write the...
 3.4.76: In Exercises 6380, find all the zeros of the function and write the...
 3.4.77: In Exercises 6380, find all the zeros of the function and write the...
 3.4.78: In Exercises 6380, find all the zeros of the function and write the...
 3.4.79: In Exercises 6380, find all the zeros of the function and write the...
 3.4.80: In Exercises 6380, find all the zeros of the function and write the...
 3.4.81: In Exercises 8186, find all the zeros of the function. When there i...
 3.4.82: In Exercises 8186, find all the zeros of the function. When there i...
 3.4.83: In Exercises 8186, find all the zeros of the function. When there i...
 3.4.84: In Exercises 8186, find all the zeros of the function. When there i...
 3.4.85: In Exercises 8186, find all the zeros of the function. When there i...
 3.4.86: In Exercises 8186, find all the zeros of the function. When there i...
 3.4.87: In Exercises 8794, use Descartess Rule of Signs to determine the po...
 3.4.88: In Exercises 8794, use Descartess Rule of Signs to determine the po...
 3.4.89: In Exercises 8794, use Descartess Rule of Signs to determine the po...
 3.4.90: In Exercises 8794, use Descartess Rule of Signs to determine the po...
 3.4.91: In Exercises 8794, use Descartess Rule of Signs to determine the po...
 3.4.92: In Exercises 8794, use Descartess Rule of Signs to determine the po...
 3.4.93: In Exercises 8794, use Descartess Rule of Signs to determine the po...
 3.4.94: In Exercises 8794, use Descartess Rule of Signs to determine the po...
 3.4.95: In Exercises 9598, use synthetic division to verify the upper and l...
 3.4.96: In Exercises 9598, use synthetic division to verify the upper and l...
 3.4.97: In Exercises 9598, use synthetic division to verify the upper and l...
 3.4.98: In Exercises 9598, use synthetic division to verify the upper and l...
 3.4.99: In Exercises 99102, find all the real zeros of the function.
 3.4.100: In Exercises 99102, find all the real zeros of the function.
 3.4.101: In Exercises 99102, find all the real zeros of the function.
 3.4.102: In Exercises 99102, find all the real zeros of the function.
 3.4.103: In Exercises 103106, find all the rational zeros of the polynomial ...
 3.4.104: In Exercises 103106, find all the rational zeros of the polynomial ...
 3.4.105: In Exercises 103106, find all the rational zeros of the polynomial ...
 3.4.106: In Exercises 103106, find all the rational zeros of the polynomial ...
 3.4.107: In Exercises 107110, match the cubic function with the numbers of r...
 3.4.108: In Exercises 107110, match the cubic function with the numbers of r...
 3.4.109: In Exercises 107110, match the cubic function with the numbers of r...
 3.4.110: In Exercises 107110, match the cubic function with the numbers of r...
 3.4.111: GEOMETRY An open box is to be made from a rectangular piece of mate...
 3.4.112: GEOMETRY A rectangular package to be sent by a delivery service (se...
 3.4.113: ADVERTISING COST A company that produces MP3 players estimates that...
 3.4.114: ADVERTISING COST A company that manufactures bicycles estimates tha...
 3.4.115: GEOMETRY A bulk food storage bin with dimensions 2 feet by 3 feet b...
 3.4.116: GEOMETRY A manufacturer wants to enlarge an existing manufacturing ...
 3.4.117: COST The ordering and transportation cost (in thousands of dollars)...
 3.4.118: HEIGHT OF A BASEBALL A baseball is thrown upward from a height of 6...
 3.4.119: PROFIT The demand equation for a certain product is where is the un...
 3.4.120: ATHLETICS The attendance (in millions) at NCAA womens college baske...
 3.4.121: It is possible for a thirddegree polynomial function with integer ...
 3.4.122: If is a zero of the function given by then must also be a zero of
 3.4.123: THINK ABOUT IT In Exercises 123128, determine (if possible) the zer...
 3.4.124: THINK ABOUT IT In Exercises 123128, determine (if possible) the zer...
 3.4.125: THINK ABOUT IT In Exercises 123128, determine (if possible) the zer...
 3.4.126: THINK ABOUT IT In Exercises 123128, determine (if possible) the zer...
 3.4.127: THINK ABOUT IT In Exercises 123128, determine (if possible) the zer...
 3.4.128: THINK ABOUT IT In Exercises 123128, determine (if possible) the zer...
 3.4.129: THINK ABOUT IT A thirddegree polynomial function has real zeros an...
 3.4.130: CAPSTONE Use a graphing utility to graph the function given by for ...
 3.4.131: THINK ABOUT IT Sketch the graph of a fifthdegree polynomial functi...
 3.4.132: WRITING Compile a list of all the various techniques for factoring ...
 3.4.133: THINK ABOUT IT Let be a quartic polynomial with leading coefficient...
 3.4.134: THINK ABOUT IT Let be a cubic polynomial with leading coefficient a...
 3.4.135: In Exercises 135 and 136, the graph of a cubic polynomial function ...
 3.4.136: In Exercises 135 and 136, the graph of a cubic polynomial function ...
 3.4.137: Use the information in the table to answer each question. (a) What ...
 3.4.138: (a) Find a quadratic function (with integer coefficients) that has ...
 3.4.139: GRAPHICAL REASONING The graph of one of the following functions is ...
Solutions for Chapter 3.4: ZEROS OF POLYNOMIAL FUNCTIONS
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 3.4: ZEROS OF POLYNOMIAL FUNCTIONS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781439048696. Chapter 3.4: ZEROS OF POLYNOMIAL FUNCTIONS includes 139 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 8. Since 139 problems in chapter 3.4: ZEROS OF POLYNOMIAL FUNCTIONS have been answered, more than 36855 students have viewed full stepbystep solutions from this chapter.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Outer product uv T
= column times row = rank one matrix.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.