Homework Help is Here – Start Your Trial Now!
Math
Algebra
108. DISCUSS: The Cubic Formula The Quadratic Formula can be used to solve any quadratic (or second-degree) equation. You might have wondered whether similar formulas exist for cubic (third-degree), quartic (fourth-degree), and higher- degree equations. For the depressed cubic x* + px +q = 0. Cardano (page 328) found the following formula for one solution: b. x = 27 2 V 4 27 A formula for quartic equations was discovered by the Ital- ian mathematician Ferrari in 1540. In 1824 the Norwegian mathematician Niels Henrik Abel proved that it is impossi- ble to write a quintic formula, that is, a formula for fifth- degree equations. Finally, Galois (page 313) gave a criterion for determining which equations can be solved by a formula involving radicals. Use the formula given above to find a solution for the fol- lowing equations. Then solve the equations using the meth- ods you learned in this section. Which method is easier? (a) x - 3x + 2 = 0 (b) x - 27x - 54 = 0 (c) x +3x + 4 = 0

108. DISCUSS: The Cubic Formula The Quadratic Formula can be used to solve any quadratic (or second-degree) equation. You might have wondered whether similar formulas exist for cubic (third-degree), quartic (fourth-degree), and higher- degree equations. For the depressed cubic x* + px +q = 0. Cardano (page 328) found the following formula for one solution: b. x = 27 2 V 4 27 A formula for quartic equations was discovered by the Ital- ian mathematician Ferrari in 1540. In 1824 the Norwegian mathematician Niels Henrik Abel proved that it is impossi- ble to write a quintic formula, that is, a formula for fifth- degree equations. Finally, Galois (page 313) gave a criterion for determining which equations can be solved by a formula involving radicals. Use the formula given above to find a solution for the fol- lowing equations. Then solve the equations using the meth- ods you learned in this section. Which method is easier? (a) x - 3x + 2 = 0 (b) x - 27x - 54 = 0 (c) x +3x + 4 = 0

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
108. DISCUSS: The Cubic Formula The Quadratic Formula can be used to solve any quadratic (or second-degree) equation. You might have wondered whether similar formulas exist for cubic (third-degree), quartic (fourth-degree), and higher- degree equations. For the depressed cubic x* + px +q = 0. Cardano (page 328) found the following formula for one solution: b. x = 27 2 V 4 27 A formula for quartic equations was discovered by the Ital- ian mathematician Ferrari in 1540. In 1824 the Norwegian mathematician Niels Henrik Abel proved that it is impossi- ble to write a quintic formula, that is, a formula for fifth- degree equations. Finally, Galois (page 313) gave a criterion for determining which equations can be solved by a formula involving radicals. Use the formula given above to find a solution for the fol- lowing equations. Then solve the equations using the meth- ods you learned in this section. Which method is easier? (a) x - 3x + 2 = 0 (b) x - 27x - 54 = 0 (c) x +3x + 4 = 0
Transcribed Image Text:108. DISCUSS: The Cubic Formula The Quadratic Formula can be used to solve any quadratic (or second-degree) equation. You might have wondered whether similar formulas exist for cubic (third-degree), quartic (fourth-degree), and higher- degree equations. For the depressed cubic x* + px +q = 0. Cardano (page 328) found the following formula for one solution: b. x = 27 2 V 4 27 A formula for quartic equations was discovered by the Ital- ian mathematician Ferrari in 1540. In 1824 the Norwegian mathematician Niels Henrik Abel proved that it is impossi- ble to write a quintic formula, that is, a formula for fifth- degree equations. Finally, Galois (page 313) gave a criterion for determining which equations can be solved by a formula involving radicals. Use the formula given above to find a solution for the fol- lowing equations. Then solve the equations using the meth- ods you learned in this section. Which method is easier? (a) x - 3x + 2 = 0 (b) x - 27x - 54 = 0 (c) x +3x + 4 = 0
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS