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The roots of a cubic equation ax'+a,x² +ax +a, =0_can be calculated using the following procedure: Set: A=az /a3, B=a\/a3, and C = a, / a 3. Calculate: D=Q' +R° , where Q = (3B – A²)/9 and R=(9AB– 27C – 2.4°) / 54 . If D>0 the equation has complex roots. If D=0 all roots are real and at least two are equal. The roots are given by:

The roots of a cubic equation ax'+a,x² +ax +a, =0_can be calculated using the following procedure: Set: A=az /a3, B=a\/a3, and C = a, / a 3. Calculate: D=Q' +R° , where Q = (3B – A²)/9 and R=(9AB– 27C – 2.4°) / 54 . If D>0 the equation has complex roots. If D=0 all roots are real and at least two are equal. The roots are given by:

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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The roots of a cubic equation azx'+a,x² +ax +a, =0 _can be calculated using the following procedure: Set: A =az /a3, B=a¡/a3, and C =a,/az. Calculate: D =Q³ +R° , where Q = (3B – A²)/9 and R=(9AB– 27C – 24°) / 54 . If D>0 the equation has complex roots. If D=0 all roots are real and at least two are equal. The roots are given by: x = 2R – A / 3, xr, = -R-A/3, and x; = -R- AI3. If D<0 all roots are real and are given by: x1 = 21 -Q cos(0 / 3) – A / 3, x, = 2/ -Q cos(0 /3 + 120°) – A / 3, and x3 = 2 -Q cos(0 / 3 +240°) – A / 3 , where cos 0 = R / -Q³. Write a MATLAB program that determines the real roots of a cubic equa- tion. As input the program asks the user to enter the values of a3, az, a1, and a, as a vector. The program then calculates the value of D. If the equations have complex roots, the message "The equation has complex roots" is dis- played. Otherwise the real roots are calculated and displayed. Use the pro- gram to solve the following equations: 5x + - 34.5x +36.9x +8.8 =0 (b) 2x + – 10x² +24x – 15 =0 (a) 2x + – 1.4x – 20.58x + 30.87 =0 (c)
Transcribed Image Text:The roots of a cubic equation azx'+a,x² +ax +a, =0 _can be calculated using the following procedure: Set: A =az /a3, B=a¡/a3, and C =a,/az. Calculate: D =Q³ +R° , where Q = (3B – A²)/9 and R=(9AB– 27C – 24°) / 54 . If D>0 the equation has complex roots. If D=0 all roots are real and at least two are equal. The roots are given by: x = 2R – A / 3, xr, = -R-A/3, and x; = -R- AI3. If D<0 all roots are real and are given by: x1 = 21 -Q cos(0 / 3) – A / 3, x, = 2/ -Q cos(0 /3 + 120°) – A / 3, and x3 = 2 -Q cos(0 / 3 +240°) – A / 3 , where cos 0 = R / -Q³. Write a MATLAB program that determines the real roots of a cubic equa- tion. As input the program asks the user to enter the values of a3, az, a1, and a, as a vector. The program then calculates the value of D. If the equations have complex roots, the message "The equation has complex roots" is dis- played. Otherwise the real roots are calculated and displayed. Use the pro- gram to solve the following equations: 5x + - 34.5x +36.9x +8.8 =0 (b) 2x + – 10x² +24x – 15 =0 (a) 2x + – 1.4x – 20.58x + 30.87 =0 (c)
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