 3.4.1: Fill in each blank so that the resulting statement is true.Consider...
 3.4.2: Fill in each blank so that the resulting statement is true.True or ...
 3.4.3: Fill in each blank so that the resulting statement is true.True or ...
 3.4.4: Fill in each blank so that the resulting statement is true.If a pol...
 3.4.5: Fill in each blank so that the resulting statement is true.If a + b...
 3.4.6: Fill in each blank so that the resulting statement is true.If a + b...
 3.4.7: Fill in each blank so that the resulting statement is true.The Line...
 3.4.8: Fill in each blank so that the resulting statement is true.Use Desc...
 3.4.9: Fill in each blank so that the resulting statement is true.Use Desc...
 3.4.10: Fill in each blank so that the resulting statement is true.Use Desc...
 3.4.11: In Exercises 916,a. List all possible rational zeros.b. Use synthet...
 3.4.12: In Exercises 916,a. List all possible rational zeros.b. Use synthet...
 3.4.13: In Exercises 916,a. List all possible rational zeros.b. Use synthet...
 3.4.14: In Exercises 916,a. List all possible rational zeros.b. Use synthet...
 3.4.15: In Exercises 916,a. List all possible rational zeros.b. Use synthet...
 3.4.16: In Exercises 916,a. List all possible rational zeros.b. Use synthet...
 3.4.17: In Exercises 1724,a. List all possible rational roots.b. Use synthe...
 3.4.18: In Exercises 1724,a. List all possible rational roots.b. Use synthe...
 3.4.19: In Exercises 1724,a. List all possible rational roots.b. Use synthe...
 3.4.20: In Exercises 1724,a. List all possible rational roots.b. Use synthe...
 3.4.21: In Exercises 1724,a. List all possible rational roots.b. Use synthe...
 3.4.22: In Exercises 1724,a. List all possible rational roots.b. Use synthe...
 3.4.23: In Exercises 1724,a. List all possible rational roots.b. Use synthe...
 3.4.24: In Exercises 1724,a. List all possible rational roots.b. Use synthe...
 3.4.25: In Exercises 2532, find an nthdegree polynomial function withreal ...
 3.4.26: In Exercises 2532, find an nthdegree polynomial function withreal ...
 3.4.27: In Exercises 2532, find an nthdegree polynomial function withreal ...
 3.4.28: In Exercises 2532, find an nthdegree polynomial function withreal ...
 3.4.29: In Exercises 2532, find an nthdegree polynomial function withreal ...
 3.4.30: In Exercises 2532, find an nthdegree polynomial function withreal ...
 3.4.31: In Exercises 2532, find an nthdegree polynomial function withreal ...
 3.4.32: In Exercises 2532, find an nthdegree polynomial function withreal ...
 3.4.33: In Exercises 3338, use Descartess Rule of Signs to determine thepos...
 3.4.34: In Exercises 3338, use Descartess Rule of Signs to determine thepos...
 3.4.35: In Exercises 3338, use Descartess Rule of Signs to determine thepos...
 3.4.36: In Exercises 3338, use Descartess Rule of Signs to determine thepos...
 3.4.37: In Exercises 3338, use Descartess Rule of Signs to determine thepos...
 3.4.38: In Exercises 3338, use Descartess Rule of Signs to determine thepos...
 3.4.39: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.40: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.41: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.42: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.43: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.44: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.45: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.46: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.47: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.48: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.49: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.50: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.51: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.52: In Exercises 3952, find all zeros of the polynomial functionor solv...
 3.4.53: Exercises 5360 show incomplete graphs of given polynomialfunctions....
 3.4.54: Exercises 5360 show incomplete graphs of given polynomialfunctions....
 3.4.55: Exercises 5360 show incomplete graphs of given polynomialfunctions....
 3.4.56: Exercises 5360 show incomplete graphs of given polynomialfunctions....
 3.4.57: Exercises 5360 show incomplete graphs of given polynomialfunctions....
 3.4.58: Exercises 5360 show incomplete graphs of given polynomialfunctions....
 3.4.59: Exercises 5360 show incomplete graphs of given polynomialfunctions....
 3.4.60: Exercises 5360 show incomplete graphs of given polynomialfunctions....
 3.4.61: A popular model of carryon luggage has a length that is10inches gr...
 3.4.62: A popular model of carryon luggage has a length that is10inches gr...
 3.4.63: Use the graph of the function modeling the volume of thecarryon lu...
 3.4.64: Use the graph of the function modeling the volume of thecarryon lu...
 3.4.65: Describe how to find the possible rational zeros of apolynomial fun...
 3.4.66: How does the linear factorization of f(x), that is,f(x) = an(x  c1...
 3.4.67: Describe how to use Descartess Rule of Signs to determinethe possib...
 3.4.68: Describe how to use Descartess Rule of Signs to determine thepossib...
 3.4.69: Why must every polynomial equation with real coefficientsof degree ...
 3.4.70: Explain why the equation x4 + 6x2 + 2 = 0 has no rationalroots.
 3.4.71: Suppose 34 is a root of a polynomial equation. What does thistell u...
 3.4.72: The equations in Exercises 7275 have real roots that are rational.U...
 3.4.73: The equations in Exercises 7275 have real roots that are rational.U...
 3.4.74: The equations in Exercises 7275 have real roots that are rational.U...
 3.4.75: The equations in Exercises 7275 have real roots that are rational.U...
 3.4.76: Use Descartess Rule of Signs to determine thepossible number of pos...
 3.4.77: Use Descartess Rule of Signs to determine thepossible number of pos...
 3.4.78: Write equations for several polynomial functions of odddegree and g...
 3.4.79: Use a graphing utility to obtain a complete graph for eachpolynomia...
 3.4.80: Use a graphing utility to obtain a complete graph for eachpolynomia...
 3.4.81: Use a graphing utility to obtain a complete graph for eachpolynomia...
 3.4.82: Use a graphing utility to obtain a complete graph for eachpolynomia...
 3.4.83: In Exercises 8386, determine whether eachstatement makes sense or d...
 3.4.84: In Exercises 8386, determine whether eachstatement makes sense or d...
 3.4.85: In Exercises 8386, determine whether eachstatement makes sense or d...
 3.4.86: In Exercises 8386, determine whether eachstatement makes sense or d...
 3.4.87: In Exercises 8790, determine whether each statement is true orfalse...
 3.4.88: In Exercises 8790, determine whether each statement is true orfalse...
 3.4.89: In Exercises 8790, determine whether each statement is true orfalse...
 3.4.90: In Exercises 8790, determine whether each statement is true orfalse...
 3.4.91: If the volume of the solid shown in the figure is 208 cubicinches, ...
 3.4.92: In this exercise, we lead you through the steps involved inthe proo...
 3.4.93: In Exercises 9396, the graph of a polynomial function isgiven.What ...
 3.4.94: In Exercises 9396, the graph of a polynomial function isgiven.What ...
 3.4.95: In Exercises 9396, the graph of a polynomial function isgiven.What ...
 3.4.96: In Exercises 9396, the graph of a polynomial function isgiven.What ...
 3.4.97: Explain why a polynomial function of degree 20 cannotcross the x@ax...
 3.4.98: Consider the equationsy1 = 1x  1  1x + 1 and y2 = 2x2  1.Find al...
 3.4.99: Write an equation in pointslope form and general form ofthe line p...
 3.4.100: Find the average rate of change of f(x) = 2x from x1 = 4to x2 = 9. ...
 3.4.101: Exercises 101103 will help you prepare for the material covered int...
 3.4.102: Exercises 101103 will help you prepare for the material covered int...
 3.4.103: Exercises 101103 will help you prepare for the material covered int...
Solutions for Chapter 3.4: Zeros of Polynomial Functions
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 3.4: Zeros of Polynomial Functions
Get Full SolutionsSince 103 problems in chapter 3.4: Zeros of Polynomial Functions have been answered, more than 30845 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra , edition: 7. College Algebra was written by and is associated to the ISBN: 9780134469164. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.4: Zeros of Polynomial Functions includes 103 full stepbystep solutions.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Column space C (A) =
space of all combinations of the columns of A.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.