 12.1: In Exercises 1 and 2 you are given polynomials p(x) and d(x). In ea...
 12.2: In Exercises 1 and 2 you are given polynomials p(x) and d(x). In ea...
 12.3: In Exercises 3 8, use synthetic division to find the quotients and ...
 12.4: In Exercises 3 8, use synthetic division to find the quotients and ...
 12.5: In Exercises 3 8, use synthetic division to find the quotients and ...
 12.6: In Exercises 3 8, use synthetic division to find the quotients and ...
 12.7: In Exercises 3 8, use synthetic division to find the quotients and ...
 12.8: In Exercises 3 8, use synthetic division to find the quotients and ...
 12.9: In Exercises 916, use synthetic division and the remainder theorem ...
 12.10: In Exercises 916, use synthetic division and the remainder theorem ...
 12.11: In Exercises 916, use synthetic division and the remainder theorem ...
 12.12: In Exercises 916, use synthetic division and the remainder theorem ...
 12.13: In Exercises 916, use synthetic division and the remainder theorem ...
 12.14: In Exercises 916, use synthetic division and the remainder theorem ...
 12.15: In Exercises 916, use synthetic division and the remainder theorem ...
 12.16: In Exercises 916, use synthetic division and the remainder theorem ...
 12.17: Find a value for a such that 3 is a root of the equation x3 4x2 ax ...
 12.18: For which values of b will 1 be a root of the equation x3 2b2 x2 x ...
 12.19: For which values of a will x 1 be a factor of the polynomial a2 x3 ...
 12.20: Use synthetic division to verify that is a root of the equation x6 ...
 12.21: Let f(x) ax3 bx2 cx d and suppose that r is a root of the equation ...
 12.22: Suppose that r is a root of the equation a2x2 a1x a0 0. Show that m...
 12.23: In Exercises 2328, list the possibilities for the rational roots of...
 12.24: In Exercises 2328, list the possibilities for the rational roots of...
 12.25: In Exercises 2328, list the possibilities for the rational roots of...
 12.26: In Exercises 2328, list the possibilities for the rational roots of...
 12.27: In Exercises 2328, list the possibilities for the rational roots of...
 12.28: In Exercises 2328, list the possibilities for the rational roots of...
 12.29: In Exercises 2936, each equation has at least one rational root. So...
 12.30: In Exercises 2936, each equation has at least one rational root. So...
 12.31: In Exercises 2936, each equation has at least one rational root. So...
 12.32: In Exercises 2936, each equation has at least one rational root. So...
 12.33: In Exercises 2936, each equation has at least one rational root. So...
 12.34: In Exercises 2936, each equation has at least one rational root. So...
 12.35: In Exercises 2936, each equation has at least one rational root. So...
 12.36: In Exercises 2936, each equation has at least one rational root. So...
 12.37: Solve the equation x3 9x2 24x 20 0, using the fact that one of the ...
 12.38: One root of the equation x2 kx 2k 0 (k 0) is twice the other. Find ...
 12.39: State each of the following theorems. (a) The division algorithm (b...
 12.40: Find a quadratic equation with roots a and a where a 1. I
 12.41: In Exercises 41 44, write each polynomial in the forman1x r1 2 1x r...
 12.42: In Exercises 41 44, write each polynomial in the forman1x r1 2 1x r...
 12.43: In Exercises 41 44, write each polynomial in the forman1x r1 2 1x r...
 12.44: In Exercises 41 44, write each polynomial in the forman1x r1 2 1x r...
 12.45: Each of Exercises 45 48 gives an equation, followed by one or more ...
 12.46: Each of Exercises 45 48 gives an equation, followed by one or more ...
 12.47: Each of Exercises 45 48 gives an equation, followed by one or more ...
 12.48: Each of Exercises 45 48 gives an equation, followed by one or more ...
 12.49: In Exercises 4954, use Descartess rule of signs to obtain informati...
 12.50: In Exercises 4954, use Descartess rule of signs to obtain informati...
 12.51: In Exercises 4954, use Descartess rule of signs to obtain informati...
 12.52: In Exercises 4954, use Descartess rule of signs to obtain informati...
 12.53: In Exercises 4954, use Descartess rule of signs to obtain informati...
 12.54: In Exercises 4954, use Descartess rule of signs to obtain informati...
 12.55: Consider the equation x3 x2 x 1 0. (a) Use Descartess rule to show ...
 12.56: Use Descartess rule to show that the equation x3 x2 3x 2 0 has no p...
 12.57: Let P be the point in the first quadrant where the curve y x3 inter...
 12.58: Let P be the point in the first quadrant where the parabola y 4 x2 ...
 12.59: Consider the equation x3 36x 84 0. (a) Use Descartess rule to check...
 12.60: Consider the equation x3 3x 1 0. (a) Use Descartess rule to check t...
 12.61: In Exercises 61 64, find polynomial equations that have integer coe...
 12.62: In Exercises 61 64, find polynomial equations that have integer coe...
 12.63: In Exercises 61 64, find polynomial equations that have integer coe...
 12.64: In Exercises 61 64, find polynomial equations that have integer coe...
 12.65: Find a fourthdegree polynomial equation with integer coefficients,...
 12.66: Find a cubic equation with integer coefficients, such that x 1 is a...
 12.67: In Exercises 6770, first determine the zeros of each function; then...
 12.68: In Exercises 6770, first determine the zeros of each function; then...
 12.69: In Exercises 6770, first determine the zeros of each function; then...
 12.70: In Exercises 6770, first determine the zeros of each function; then...
 12.71: For Exercises 7178, carry out the indicated operations, and express...
 12.72: For Exercises 7178, carry out the indicated operations, and express...
 12.73: For Exercises 7178, carry out the indicated operations, and express...
 12.74: For Exercises 7178, carry out the indicated operations, and express...
 12.75: For Exercises 7178, carry out the indicated operations, and express...
 12.76: For Exercises 7178, carry out the indicated operations, and express...
 12.77: For Exercises 7178, carry out the indicated operations, and express...
 12.78: For Exercises 7178, carry out the indicated operations, and express...
 12.79: The real part of a complex number z is denoted by Re(z). For instan...
 12.80: The imaginary part of a complex number z is denoted by Im(z). For i...
 12.81: The absolute value of the complex number a bi is defined by a bi (a...
 12.82: In Exercises 82 86, verify that the formulas are correct by carryin...
 12.83: In Exercises 82 86, verify that the formulas are correct by carryin...
 12.84: In Exercises 82 86, verify that the formulas are correct by carryin...
 12.85: In Exercises 82 86, verify that the formulas are correct by carryin...
 12.86: In Exercises 82 86, verify that the formulas are correct by carryin...
 12.87: In Exercises 8792, determine the partial fraction decomposition for...
 12.88: In Exercises 8792, determine the partial fraction decomposition for...
 12.89: In Exercises 8792, determine the partial fraction decomposition for...
 12.90: In Exercises 8792, determine the partial fraction decomposition for...
 12.91: In Exercises 8792, determine the partial fraction decomposition for...
 12.92: In Exercises 8792, determine the partial fraction decomposition for...
 12.93: (a) Let f(x) x4 2x3 x2 1. Use the equatingthecoefficients theorem ...
 12.94: (a) Compute the product (x2 rx c)(x2 rx c). [This can be useful in ...
Solutions for Chapter 12: Roots of Polynomial Equations
Full solutions for Precalculus: With Unit Circle Trigonometry (with Interactive Video Skillbuilder CDROM) (Available 2010 Titles Enhanced Web Assign)  4th Edition
ISBN: 9780534402303
Solutions for Chapter 12: Roots of Polynomial Equations
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Precalculus: With Unit Circle Trigonometry (with Interactive Video Skillbuilder CDROM) (Available 2010 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780534402303. Chapter 12: Roots of Polynomial Equations includes 94 full stepbystep solutions. Since 94 problems in chapter 12: Roots of Polynomial Equations have been answered, more than 25426 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus: With Unit Circle Trigonometry (with Interactive Video Skillbuilder CDROM) (Available 2010 Titles Enhanced Web Assign), edition: 4.

Absolute value of a vector
See Magnitude of a vector.

Additive inverse of a complex number
The opposite of a + bi, or a  bi

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Arctangent function
See Inverse tangent function.

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Conversion factor
A ratio equal to 1, used for unit conversion

Descriptive statistics
The gathering and processing of numerical information

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

nset
A set of n objects.

Obtuse triangle
A triangle in which one angle is greater than 90°.

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Real axis
See Complex plane.

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

Zero factorial
See n factorial.