 4.5.1: In Exercises 18, find all zeros (real and complex). Factor the poly...
 4.5.2: In Exercises 18, find all zeros (real and complex). Factor the poly...
 4.5.3: In Exercises 18, find all zeros (real and complex). Factor the poly...
 4.5.4: In Exercises 18, find all zeros (real and complex). Factor the poly...
 4.5.5: In Exercises 18, find all zeros (real and complex). Factor the poly...
 4.5.6: In Exercises 18, find all zeros (real and complex). Factor the poly...
 4.5.7: In Exercises 18, find all zeros (real and complex). Factor the poly...
 4.5.8: In Exercises 18, find all zeros (real and complex). Factor the poly...
 4.5.9: In Exercises 916, a polynomial function with real coefficients is d...
 4.5.10: In Exercises 916, a polynomial function with real coefficients is d...
 4.5.11: In Exercises 916, a polynomial function with real coefficients is d...
 4.5.12: In Exercises 916, a polynomial function with real coefficients is d...
 4.5.13: In Exercises 916, a polynomial function with real coefficients is d...
 4.5.14: In Exercises 916, a polynomial function with real coefficients is d...
 4.5.15: In Exercises 916, a polynomial function with real coefficients is d...
 4.5.16: In Exercises 916, a polynomial function with real coefficients is d...
 4.5.17: In Exercises 1722, find a polynomial of minimum degree that has the...
 4.5.18: In Exercises 1722, find a polynomial of minimum degree that has the...
 4.5.19: In Exercises 1722, find a polynomial of minimum degree that has the...
 4.5.20: In Exercises 1722, find a polynomial of minimum degree that has the...
 4.5.21: In Exercises 1722, find a polynomial of minimum degree that has the...
 4.5.22: In Exercises 1722, find a polynomial of minimum degree that has the...
 4.5.23: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.24: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.25: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.26: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.27: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.28: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.29: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.30: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.31: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.32: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.33: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.34: In Exercises 2334, given a zero of the polynomial, determine all ot...
 4.5.35: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.36: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.37: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.38: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.39: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.40: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.41: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.42: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.43: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.44: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.45: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.46: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.47: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.48: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.49: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.50: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.51: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.52: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.53: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.54: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.55: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.56: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.57: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.58: In Exercises 3558, factor each polynomial as a product of linear fa...
 4.5.59: If the profit function of a given company has all imaginary zeros a...
 4.5.60: If the profit function of a given company has all imaginary zeros a...
 4.5.61: If the profit function of a company is modeled by a thirddegree po...
 4.5.62: If the profit function of a company is modeled by a thirddegree po...
 4.5.63: If the profit function pictured is a thirddegree polynomial, how m...
 4.5.64: If the profit function pictured is a fourthdegree polynomial with ...
 4.5.65: If the concentration function pictured is a thirddegree polynomial...
 4.5.66: If the concentration function pictured is a fourthdegree polynomia...
 4.5.67: Given that 1 is a zero of P(x) x3 2x2 7x 6, find all other zeros. S...
 4.5.68: Factor the polynomial P(x) 2x3 x2 2x 1. Solution: Step 1: Since P(x...
 4.5.69: If x 1 is a zero of a polynomial function, then x 1 is also a zero ...
 4.5.70: All zeros of a polynomial function correspond to xintercepts
 4.5.71: A polynomial function of degree n, n 0 must have at least one zero.
 4.5.72: A polynomial function of degree n, n 0 can be written as a product ...
 4.5.73: s it possible for an odddegree polynomial to have all imaginary co...
 4.5.74: Is it possible for an evendegree polynomial to have all imaginary ...
 4.5.75: Find a polynomial function that has degree 6, and for which bi is a...
 4.5.76: Find a polynomial function that has degree 4, and for which a bi is...
 4.5.77: For Exercises 77 and 78, determine possible combinations of real an...
 4.5.78: For Exercises 77 and 78, determine possible combinations of real an...
 4.5.79: For Exercises 79 and 80, find all zeros (real and complex). Factor ...
 4.5.80: For Exercises 79 and 80, find all zeros (real and complex). Factor ...
Solutions for Chapter 4.5: Complex Zeros: The Fundamental Theorem of Algebra
Full solutions for Algebra and Trigonometry,  3rd Edition
ISBN: 9780840068132
Solutions for Chapter 4.5: Complex Zeros: The Fundamental Theorem of Algebra
Get Full SolutionsChapter 4.5: Complex Zeros: The Fundamental Theorem of Algebra includes 80 full stepbystep solutions. Since 80 problems in chapter 4.5: Complex Zeros: The Fundamental Theorem of Algebra have been answered, more than 44841 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry, was written by and is associated to the ISBN: 9780840068132. This textbook survival guide was created for the textbook: Algebra and Trigonometry,, edition: 3.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row

Equilibrium point
A point where the supply curve and demand curve intersect. The corresponding price is the equilibrium price.

Identity function
The function ƒ(x) = x.

Irrational numbers
Real numbers that are not rational, p. 2.

Leading coefficient
See Polynomial function in x

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Permutation
An arrangement of elements of a set, in which order is important.

Real part of a complex number
See Complex number.

Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

Righthand limit of ƒ at x a
The limit of ƒ as x approaches a from the right.

Rigid transformation
A transformation that leaves the basic shape of a graph unchanged.

Slant line
A line that is neither horizontal nor vertical

Slopeintercept form (of a line)
y = mx + b

Solve a system
To find all solutions of a system.

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.