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ERIC Number: EJ993836
Record Type: Journal
Publication Date: 2012
Pages: 3
Abstractor: As Provided
ISSN: ISSN-0020-739X
Self-Replicating Quadratics
Withers, Christopher S.; Nadarajah, Saralees
International Journal of Mathematical Education in Science and Technology, v43 n4 p559-561 2012
We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript 1/N], namely Q(w[superscript 1; subscript N]x[superscript 1/N]) x Q(w[superscript 2; subscript N ]x[superscript 1/N]) ... Q(w[superscript N ; subscript N]x[superscript 1/N]), where "w[subscript n]" is the "N"th root of 1.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A