P Prerequisites 1 Equations, Inequalities, And Modeling 2 Functions And Graphs 3 Polynomial And Rational Functions 4 Exponential And Logarithmic Functions 5 Systems Of Equations And Inequalities 6 Matrices And Determinants 7 The Conic Sections 8 Sequences, Series, And Probability A Scatter Diagrams And Curve Fitting expand_more
3.1 Quadratic Functions And Inequalities 3.2 Zeros Of Polynomial Functions 3.3 The Theory Of Equations 3.4 Graphs Of Polynomial Functions 3.5 Rational Functions And Inequalities Chapter Questions expand_more
Problem 1FT: True or False? Explain. The number 1 is a root of x3 –1 = 0 with multiplicity 3. Problem 2FT Problem 3FT Problem 4FT Problem 5FT Problem 6FT Problem 7FT Problem 8FT Problem 9FT: True or False? Explain.
9. The equation x3 –5x2 + 6x –1 = 0 has no negative roots.
Problem 10FT: True or False? Explain. The equation 5x3 – 171 = 0 has two imaginary solutions. Problem 1E Problem 2E Problem 3E: Fill in the blank. If P(x) = 0 is a polynomial equation with real coefficients and the complex... Problem 4E Problem 5E Problem 6E Problem 7E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 8E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 9E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 10E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 11E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 12E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 13E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 14E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 15E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 16E: State the degree of each polynomial equation. Find all of the real and imaginary roots of each... Problem 17E: Find each product.
17.
Problem 18E: Find each product.
18.
Problem 19E: Find each product. Problem 20E: Find each product. Problem 21E: Find each product. Problem 22E: Find each product. Problem 23E: Find each product.
23.
Problem 24E: Find each product.
24.
Problem 25E: Find a polynomial equation with real coefficients that has the given roots.
25. –3, 5
Problem 26E: Find a polynomial equation with real coefficients that has the given roots. 6, –1 Problem 27E: Find a polynomial equation with real coefficients that has the given roots. –4i, 4i Problem 28E: Find a polynomial equation with real coefficients that has the given roots.
28. -9i, 9i
Problem 29E: Find a polynomial equation with real coefficients that has the given roots. 3 – i Problem 30E: Find a polynomial equation with real coefficients that has the given roots. 4 + i Problem 31E: Find a polynomial equation with real coefficients that has the given roots. 4, -i Problem 32E: Find a polynomial equation with real coefficients that has the given roots.
32. 4, -i
Problem 33E: Find a polynomial equation with real coefficients that has the given roots. Problem 34E: Find a polynomial equation with real coefficients that has the given roots. Problem 35E: Find a polynomial equation with real coefficients that has the given roots.
35. 3, 1– i
Problem 36E: Find a polynomial equation with real coefficients that has the given roots. 5, 4 – 3i Problem 37E: Find a polynomial equation with real coefficients that has the given roots. 1, 2, 3 Problem 38E: Find a polynomial equation with real coefficients that has the given roots. –1, 2, –3 Problem 39E: Find a polynomial equation with real coefficients that has the given roots. 1, 2 – 3i Problem 40E: Find a polynomial equation with real coefficients that has the given roots. –1, 4 – 2i Problem 41E: Find a polynomial equation with real coefficients that has the given roots.
41.
Problem 42E: Find a polynomial equation with real coefficients that has the given roots. Problem 43E: Find a polynomial equation with real coefficients that has the given roots. i, 1 + i Problem 44E: Find a polynomial equation with real coefficients that has the given roots. 3i, 3 – i Problem 45E: Use Descartes’s rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 46E: Use Descartes’s rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 47E: Use Descartes's rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 48E: Use Descartes’s rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 49E: Use Descartes’s rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 50E: Use Descartes’s rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 51E: Use Descartes’s rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 52E: Use Descartes’s rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 53E: Use Descartes's rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 54E: Use Descartes’s rule of signs to discuss the possibilities for the of each equation. Do not solve... Problem 55E: Use the theorem on bounds to establish the best integral bounds for the roots of each equation.
55.... Problem 56E: Use the theorem on bounds to establish the best integral bounds for the roots of each equation. Problem 57E: Use the theorem on bounds to establish the best integral bounds for the roots of each equation.
57.... Problem 58E: Use the theorem on bounds to establish the best integral bounds for the roots of each equation.
58.... Problem 59E: Use the theorem on hounds to establish the best integral bounds for the roots of each equation. Problem 60E: Use the theorem on bounds to establish the best integral bounds for the roots of each equation.
60.... Problem 61E: Use the theorem on bounds to establish the best integral bounds for the roots of each equation. Problem 62E: Use the theorem on bounds to establish the best integral bounds for the roots of each equation.
62.... Problem 63E: Use the rational zero theorem, Descartes's rule of signs, and the theorem on bounds as aids in... Problem 64E Problem 65E Problem 66E: Use the rational zero theorem, Descartes's rule of signs, and the theorem on bounds as aids in... Problem 67E: Use the rational zero theorem, Descartes's rule of signs, and the theorem on bounds as aids in... Problem 68E Problem 69E Problem 70E Problem 71E: Use the rational zero theorem, Descartes's rule of signs, and the theorem on bounds as aids in... Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E: For each of the following functions use synthetic division and the theorem on bounds to find... Problem 80E Problem 81E Problem 82E: For each of the following functions use synthetic division and the theorem on bounds to find... Problem 83E: For each of the following functions use synthetic division and the theorem on bounds to find... Problem 84E: For each of the following functions use synthetic division and the theorem on bounds to find... Problem 85E: Solve each problem. Growth Rate for Bacteria The instantaneous growth rate of a population is the... Problem 86E Problem 87E Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E Problem 97E Problem 98E Problem 99E Problem 100E Problem 101E: Solve each problem.
101. Packing Billiard Balls There are several ways to tightly pack nine billiard... Problem 102E Problem 1PQ: Find all real and imaginary roots to x5–x3 = 0, including multiplicities. Problem 2PQ Problem 3PQ Problem 4PQ Problem 5PQ Problem LC format_list_bulleted