 12.5.1: (a) State the rational roots theorem. (b) List the possibilities fo...
 12.5.2: Use the rational roots theorem to list the possibilities for the ra...
 12.5.3: (a) Use the rational roots theorem to explain why the equation x5 1...
 12.5.4: (a) The graph in the following figure indicates that 4 may be a roo...
 12.5.5: In Exercises 510, list the possibilities for rational roots.
 12.5.6: In Exercises 510, list the possibilities for rational roots.
 12.5.7: In Exercises 510, list the possibilities for rational roots.
 12.5.8: In Exercises 510, list the possibilities for rational roots.
 12.5.9: In Exercises 510, list the possibilities for rational roots.
 12.5.10: In Exercises 510, list the possibilities for rational roots.
 12.5.11: In Exercises 1116, show that each equation has no rational roots.
 12.5.12: In Exercises 1116, show that each equation has no rational roots.
 12.5.13: In Exercises 1116, show that each equation has no rational roots.
 12.5.14: In Exercises 1116, show that each equation has no rational roots.
 12.5.15: In Exercises 1116, show that each equation has no rational roots.
 12.5.16: In Exercises 1116, show that each equation has no rational roots.
 12.5.17: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.18: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.19: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.20: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.21: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.22: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.23: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.24: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.25: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.26: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.27: For Exercises 1727, find the rational roots of each equation, and t...
 12.5.28: In Exercises 28 and 29, determine integral upper and lower bounds f...
 12.5.29: In Exercises 28 and 29, determine integral upper and lower bounds f...
 12.5.30: Referring to equation (1) in this section, multiply out the leftha...
 12.5.31: In Exercises 3136, each equation has exactly one positive root. In ...
 12.5.32: In Exercises 3136, each equation has exactly one positive root. In ...
 12.5.33: In Exercises 3136, each equation has exactly one positive root. In ...
 12.5.34: In Exercises 3136, each equation has exactly one positive root. In ...
 12.5.35: In Exercises 3136, each equation has exactly one positive root. In ...
 12.5.36: In Exercises 3136, each equation has exactly one positive root. In ...
 12.5.37: In Exercises 37 40, each polynomial equation has exactly one negati...
 12.5.38: In Exercises 37 40, each polynomial equation has exactly one negati...
 12.5.39: In Exercises 37 40, each polynomial equation has exactly one negati...
 12.5.40: In Exercises 37 40, each polynomial equation has exactly one negati...
 12.5.41: This exercise outlines a proof of the rational roots theorem. At on...
 12.5.42: The location theorem asserts that the polynomial equation f(x) 0 ha...
 12.5.43: In Exercises 43 47, first graph the two functions. Then use the met...
 12.5.44: In Exercises 43 47, first graph the two functions. Then use the met...
 12.5.45: In Exercises 43 47, first graph the two functions. Then use the met...
 12.5.46: In Exercises 43 47, first graph the two functions. Then use the met...
 12.5.47: In Exercises 43 47, first graph the two functions. Then use the met...
 12.5.48: In a note that appeared in The TwoYear College Mathematics Journal...
 12.5.49: In a note that appeared in The College Mathematics Journal [vol. 20...
 12.5.50: The following result is a particular case of a theorem proved by Pr...
 12.5.51: (a) Use a calculator to verify that the number tan 9 appears to be ...
 12.5.52: As background for this exercise you need to have worked Exercise 51...
 12.5.53: (a) Let u 2p/7. Use the reference angle concept to explain why cos ...
 12.5.54: In Exercises 54 58 you need to know that a prime number is a positi...
 12.5.55: In Exercises 54 58 you need to know that a prime number is a positi...
 12.5.56: In Exercises 54 58 you need to know that a prime number is a positi...
 12.5.57: In Exercises 54 58 you need to know that a prime number is a positi...
 12.5.58: In Exercises 54 58 you need to know that a prime number is a positi...
 12.5.59: Find all integral values of b for which the equation x3 b2 x2 3bx 4...
 12.5.60: Let f(x) x3 3x2 x 3. (a) Factor f(x) by using the basic factoring t...
Solutions for Chapter 12.5: RATIONAL AND IRRATIONAL ROOTS
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 12.5: RATIONAL AND IRRATIONAL ROOTS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 60 problems in chapter 12.5: RATIONAL AND IRRATIONAL ROOTS have been answered, more than 25472 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. Chapter 12.5: RATIONAL AND IRRATIONAL ROOTS includes 60 full stepbystep 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.

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

Factored form
The left side of u(v + w) = uv + uw.

Geometric series
A series whose terms form a geometric sequence.

Grapher or graphing utility
Graphing calculator or a computer with graphing software.

Graphical model
A visible representation of a numerical or algebraic model.

Imaginary part of a complex number
See Complex number.

Independent variable
Variable representing the domain value of a function (usually x).

Inequality symbol or
<,>,<,>.

Infinite limit
A special case of a limit that does not exist.

Leading term
See Polynomial function in x.

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Quadratic equation in x
An equation that can be written in the form ax 2 + bx + c = 01a ? 02

Sum of an infinite series
See Convergence of a series

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Wrapping function
The function that associates points on the unit circle with points on the real number line

Zero factor property
If ab = 0 , then either a = 0 or b = 0.