Concept explainers
The three cube roots of +1 are often called
Show that this is reasonable, that is, show that the cube roots of +1 are +1 and two other numbers, each of which is the square of the other.
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Mathematical Methods in the Physical Sciences
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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.arrow_forwardDetermine the number and nature of the roots of the equation in Exercise 67. Calculate the discriminant associated with the equation 6x2+5x+1=0.arrow_forward
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