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The probability certain random quadratics have real roots

Published online by Cambridge University Press:  13 October 2021

Chris Boucher
Chris Boucher*
Affiliation:
Mathematics Department, Salem State University, 352 Lafayette Street, Salem, MA 01970 USA, e-mail: cboucher@salemstate.edu
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Extract

Early in high school algebra, quadratics chosen as examples by teachers and textbooks alike tend to have integer coefficients and to factorise over the integers. This can give the misleading impression that such quadratics are the norm. As students progress into calculus and begin regularly seeing quadratics that are not as ‘nice’, we hope they become disabused of this notion. Indeed, even if the coefficients of the quadratic are integers, the probability that the quadratic factorises over the integers tends to zero as the range from which the integers are drawn grows (see [1]). But what if we ask about a behaviour less restrictive than factorising, say merely having real roots? This is the problem that concerns this Article.

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 564 , November 2021 , pp. 410 - 415
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Copyright
© The Mathematical Association 2021

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References

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