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2534. A geometrical picture of the set of all real quadratic polynomials

Published online by Cambridge University Press:  03 November 2016

Hazel Perfect
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Abstract

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Type
Mathematical Notes
Information
The Mathematical Gazette , Volume 39 , Issue 329 , September 1955 , pp. 212 - 214
Copyright
Copyright © The Mathematical Association 1955

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References

(page no 213 note *) This result is often used. (Of course, it is simple to prove algebraically, but the geometry makes it obvious.) E.g. a standard method of transforming the integral ∫(ax 2 + bx + c)–1(a'x 2 + b'x + c')–½ dx, where b 2 < 4ac, is to put x = (λ +μt)/(1 + t), where λ, μ are the roots of the jacobian of ax 2 + bx + c and a'x 2 + b'x + c'