When Do The Quadratic Polynomials px^2+qy+r And 2px^2+qy+r Both Factor?

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dc.contributor.author Brooke Hatanaka
dc.date.accessioned 2018-01-23T20:22:07Z
dc.date.available 2018-01-23T20:22:07Z
dc.date.issued 04/11/2015
dc.identifier.uri http://hdl.handle.net/20.500.12088/7602
dc.description dc.description
dc.description.abstract One mathematical skill developed in a high school algebra class involves factoring a quadratic polynomial into a product of two binomials. For example, x^2+17x+30=(x+2)(x+15). If a 2 is placed in front of the x^2, the polynomial 2x^2+17x+30 factors as(2x+5)(x+6). A good exercise for students is to find other quadratic polynomials?px?^2+qy+r and?2px?^2+qy+r that both factor. A pair of quadratic polynomials with this property is called a quadratic doublet. The first part of this talk will characterize values for p, q, and r that yield quadratic doublets. A Pythagorean Triple is three whole numbers a, b, c with the property that a^2+b^2=c^2 . The second part of the talk will show a connection between the quadratic doublets and Pythagorean Triples.
dc.description.sponsorship Vincent Ferlini
dc.language.iso en_US
dc.publisher Keene State College
dc.subject Mathematics
dc.title When Do The Quadratic Polynomials px^2+qy+r And 2px^2+qy+r Both Factor?
dc.type Presentation

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