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The Geometry of the Discriminant of a Polynomial

1996
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Mathematical Gazette
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1 Our theme E VERYONE knows that the condition for the quadratic ax 2 + bx + c to have two equal roots, i.e. to have a repeated root, is that its discriminant ∂ 2 = b 2 − 4ac should be zero. We should remark, at the outset, that we are concerned only with ordinary polynomials whose coefficients are complex numbers. Indeed, little is lost if a reader assumes that all our polynomials are real, i.e. have real numbers for all their coefficients, though their complex roots must be considered as well

doi:10.2307/3619560
fatcat:l3chdz7xjzgbxl7otyllk3uiwm