Questions 1-10 are concerned with the equation: +62 +9y = 9x dt 4. The equation is homogeneous. a. True b. False 5. The equation has variable coefficients. a. True b. False 6. The roots of the characteristic equation are: a. Real and unequal b. Real and equal d²y dt² c. Complex d. Complex conjugates

Questions 1-10 are concerned with the equation: +62 +9y = 9x dt 4. The equation is homogeneous. a. True b. False 5. The equation has variable coefficients. a. True b. False 6. The roots of the characteristic equation are: a. Real and unequal b. Real and equal d²y dt² c. Complex d. Complex conjugates

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section8.4: Roots Of A Complex Number

Problem 41PS: Recall from the introduction to Section 8.2 that Jerome Cardans solutions to the equation x3=15x+4...

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Recall from the introduction to Section 8.2 that Jerome Cardans solutions to the equation x3=15x+4 could be written as x=2+11i3+211i3 Lets assume that the two cube roots are complex conjugates. If they are, then we can simplify our work by noticing that x=2+11i3+211i3=a+bi+abi=2a which means that we simply double the real part of each cube root of 2+11i to find the solutions to x3=15x+4. Now, to end our work with Cardan, find the three cube roots of 2+11i. Then, noting the discussion above, use the three cube roots to solve the equation x3=15x+4. Write your answers accurate to the nearest thousandth.
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