10. Consider the following questions about roots. (a) What property must a number have to be a "square root of 25"? Of what poly- nomial is it a root? List all the roots of this polynomial (including nonreal roots in C). Which of these roots should be called the square root of 25? (b) Repeat part (a) for cube roots of 8. (c) Repeat part (a) for cube roots of -8. (d) Repeat part (a) for square roots of -25.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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10. Consider the following questions about roots.
(a) What property must a number have to be a "square root of 25"? Of what poly-
nomial is it a root? List all the roots of this polynomial (including nonreal roots
in C). Which of these roots should be called the square root of 25?
(b) Repeat part (a) for cube roots of 8.
(c) Repeat part (a) for cube roots of -8.
(d) Repeat part (a) for square roots of -25.
Transcribed Image Text:10. Consider the following questions about roots. (a) What property must a number have to be a "square root of 25"? Of what poly- nomial is it a root? List all the roots of this polynomial (including nonreal roots in C). Which of these roots should be called the square root of 25? (b) Repeat part (a) for cube roots of 8. (c) Repeat part (a) for cube roots of -8. (d) Repeat part (a) for square roots of -25.
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