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Learn how to pronounce discriminant
discriminant
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A binary form which has a square factor has its discriminant equal to zero.
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To express the function aoa2 - _ which is the discriminant of the binary quadratic aoxi -+-2a1x2x2-+a2x2 = ai =1, 1, in a symbolic form we have 2(aoa 2 -ai) =aoa2 +aGa2 -2 a1 � al = a;b4 -}-alb?
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The Binary Quadratic.-The complete system consists of the form itself, ax, and the discriminant, which is the second transvectant of the form upon itself, viz.: (f, f') 2 = (ab) 2; or, in real coefficients, 2(a 0 a 2 a 2 1).
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This follows at once from the fact that the discriminant is Mara s) 2 II(/3, -fis)2{II(ar-/3$)}2.
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The expression (ab) 4 properly appertains to a quartic; for a quadratic it may also be written (ab) 2 (cd) 2 , and would denote the square of the discriminant to a factor pres.
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