An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 220
... Sturm's Theorem . Denote the first member of the equation x2 + a xn - 1 + & c . 0 by u and its derivative by U. Find the greatest common divisor of u and U , and , in performing this process , let the several remainders which are of con ...
... Sturm's Theorem . Denote the first member of the equation x2 + a xn - 1 + & c . 0 by u and its derivative by U. Find the greatest common divisor of u and U , and , in performing this process , let the several remainders which are of con ...
Page 221
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Sturm's Theorem . Find the row of signs ... Sturm's Theorem . corresponding to the value q of the 19 * CH . VIII . § III . ] 221 REAL ROOTS .
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Sturm's Theorem . Find the row of signs ... Sturm's Theorem . corresponding to the value q of the 19 * CH . VIII . § III . ] 221 REAL ROOTS .
Page 222
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Sturm's Theorem . corresponding to the value ... Sturm's Theorem . of the two limits p and q 222 [ CH . VIII . § III . ALGEBRA .
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Sturm's Theorem . corresponding to the value ... Sturm's Theorem . of the two limits p and q 222 [ CH . VIII . § III . ALGEBRA .
Page 223
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Sturm's Theorem . of the two limits p and q , than in the row which corre- sponds to the less of these two limits , by a number which is exactly equal to the number ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Sturm's Theorem . of the two limits p and q , than in the row which corre- sponds to the less of these two limits , by a number which is exactly equal to the number ...
Page 224
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Sturm's Theorem . 292. EXAMPLES . 1. Find the number of real roots of the equation 2 x4 20 x + 19 = 0 and also the number contained between 1 and 2 . Solution . In ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Sturm's Theorem . 292. EXAMPLES . 1. Find the number of real roots of the equation 2 x4 20 x + 19 = 0 and also the number contained between 1 and 2 . Solution . In ...
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126 become zero 3d root arithmetical mean arithmetical progression Binomial Theorem coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence