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S1. Assume 6² - 4ac <0 in ar²+bx+c, what is the imaginary part of the root?

S1. Assume 6² - 4ac <0 in ar²+bx+c, what is the imaginary part of the root?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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S1. Assume 6² - 4ac <0 in ar²+bx+c, what is the imaginary part of the root? S2. Assume 6² - 4ac <0 in ax²+bx+c, show that the 2 roots must be complex conjugates. S3. Solve the IVP and graph the solution: y" + 2y + 2y = 0 y (0) = 0, y'(0) = 1 While the solution is not a periodic function, it does cross the axis at regular intervals. So find all the roots of the solution, and compute the distance between successive roots to see that it is a constant.
Transcribed Image Text:S1. Assume 6² - 4ac <0 in ar²+bx+c, what is the imaginary part of the root? S2. Assume 6² - 4ac <0 in ax²+bx+c, show that the 2 roots must be complex conjugates. S3. Solve the IVP and graph the solution: y" + 2y + 2y = 0 y (0) = 0, y'(0) = 1 While the solution is not a periodic function, it does cross the axis at regular intervals. So find all the roots of the solution, and compute the distance between successive roots to see that it is a constant.
Expert Solution
Step 1

S1: The expression is ax2+bx+c and the condition is b2-4ac<0.

To describe: The imaginary part of the root.

S2: The expression is ax2+bx+c and the condition is b2-4ac<0.

To show that the two roots must be complex conjugate.

S3: Solve the initial value problem is: y''+2y'+2y=0; y0=0, y'0=1.

Also, find all the roots of the solution, and compute the distance between successive roots to see that it is a constant.

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