Explanation Formula used: The solution of the cubic equation of the form x 3 + a x 2 + b x + c = 0 is given by, A 3 + B 3 − a 3 , ω A 3 + ω 2 B 3 − a 3 , and ω 2 A 3 + ω B 3 − a 3 where, ω = − 1 + i 3 2 , p = b − a 2 3 , q = c − a b 3 + 2 a 3 27 A = − q 2 + ( q 2 ) 2 + ( p 3 ) 3 , B = − q 2 − ( q 2 ) 2 + ( p 3 ) 3 Select A and B such that A 3 B 3 = − p 3 . Calculation: The given equation is x 3 − 6 x 2 + 33 x − 92 = 0 . Compare the given equation with x 3 + a x 2 + b x + c = 0 . Here a = − 6 , b = 33 and c = − 92 . The value of ω is given by, ω = − 1 + i 3 2 Substitute − 6 for a , 33 for b and − 92 for c to solve for the value of p , p = b − a 2 3 = 33 − ( − 6 ) 2 3 = 33 − 12 = 21 Substitute − 6 for a , 33 for b and − 92 for c to solve for the value of q , q = c − a b 3 + 2 a 3 27 = − 92 − ( − 6 ) ( 33 ) 3 + 2 ( − 6 ) 3 27 = − 92 + 66 − 16 = − 42 Substitute 21 for p and − 42 for q to solve for the value of A , A = − q 2 + ( q 2 ) 2 + ( p 3 ) 3 = − ( − 42 ) 2 + ( − 42 2 ) 2 + ( 21 3 ) 3 = 21 + 441 + 343 = 49 Substitute 21 for p and 49 for q to solve for the value of B , B = − q 2 − ( q 2 ) 2 + ( p 3 ) 3 = − ( − 42 ) 2 − ( −

8th Edition

ISBN: 9781285463230

Author: Gilbert, Linda, Jimmie

Publisher: Cengage Learning,

See similar textbooks

Videos

Question

Chapter 8.5, Problem 11E

To determine

To calculate: The solutions of the equation x3−6x2+33x−92=0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.5, Problem 10E

Chapter 8.5, Problem 12E

Students have asked these similar questions

1. For the following subsets of R3, explain whether or not they are a subspace of R³. (a) (b) 1.1 0.65 U = span -3.4 0.23 0.4 -0.44 0 (})} a V {(2) | ER (c) Z= the points in the z-axis

Solve the following equation forx. leave answer in Simplified radical form. 5x²-4x-3=6

MATCHING LIST Question 6 Listen Use the given equations and their discriminants to match them to the type and number of solutions. 00 ed two irrational solutions a. x²+10x-2=-24 two rational solutions b. 8x²+11x-3=7 one rational solution c. 3x²+2x+7=2 two non-real solutions d. x²+12x+45 = 9 DELL FLOWER CHILD 10/20 All Changes S $681 22991

Chapter 8 Solutions

Elements Of Modern Algebra

Ch. 8.1 - True or False Label each of the following...Ch. 8.1 - Prob. 2TFE Ch. 8.1 - Prob. 3TFE Ch. 8.1 - Prob. 4TFE Ch. 8.1 - Prob. 5TFE Ch. 8.1 - Prob. 6TFE Ch. 8.1 - Prob. 7TFE Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The solutions of the equation x 3 − 6 x 2 + 33 x − 92 = 0 .

Solution Summary: The author explains the formula used to calculate the solutions of the cubic equation x3+a x +bx+c=0.

Videos

To calculate: The solutions of the equation x3−6x2+33x−92=0.

Want to see the full answer?

Chapter 8 Solutions