An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 241
... Commensurable Root is a real root , which can be exactly expressed by whole numbers or frac- tions . 311. Problem . To find the commensurable ... root must 21 CH . VIII . § III . ] 241 REAL ROOTS .
... Commensurable Root is a real root , which can be exactly expressed by whole numbers or frac- tions . 311. Problem . To find the commensurable ... root must 21 CH . VIII . § III . ] 241 REAL ROOTS .
Page 242
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Method of finding Integral Roots ... commensurable root of the given equa- tion must be an integer . Again , the ... Roots . In the same way 242 [ CH . VIII . III .
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Method of finding Integral Roots ... commensurable root of the given equa- tion must be an integer . Again , the ... Roots . In the same way 242 [ CH . VIII . III .
Page 243
... roots which give -p for the value of this quantity . 312. EXAMPLES . 1. Find the commensurable roots of the equation 25 19x334x2 + 12 x — 40 = 0 . - - Solution . The extreme limits of the real roots are + 7 · 4 , and -6.9 . Hence we ...
... roots which give -p for the value of this quantity . 312. EXAMPLES . 1. Find the commensurable roots of the equation 25 19x334x2 + 12 x — 40 = 0 . - - Solution . The extreme limits of the real roots are + 7 · 4 , and -6.9 . Hence we ...
Page 244
... Commensurable Roots of any Equation . -40 ; 5 , 4 , 2 , 1 , - 1 , ― 4 , 2 , -8 , -28 , 52 , - 4 , 32 , 22 , 6 , -18 ... roots of the given equation , and its first member , divided by the factor -- ( x - 2 ) ( x + 1 ) ( x + 5 ) = x3 + 4 ...
... Commensurable Roots of any Equation . -40 ; 5 , 4 , 2 , 1 , - 1 , ― 4 , 2 , -8 , -28 , 52 , - 4 , 32 , 22 , 6 , -18 ... roots of the given equation , and its first member , divided by the factor -- ( x - 2 ) ( x + 1 ) ( x + 5 ) = x3 + 4 ...
Page 245
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Commensurable Roots of any Equation . 6. Find all the roots of the equation x53x48x3 + 24 x2-9x + 27 = 0 which has commensurable and equal roots . Ans . 3 , -3 ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Commensurable Roots of any Equation . 6. Find all the roots of the equation x53x48x3 + 24 x2-9x + 27 = 0 which has commensurable and equal roots . Ans . 3 , -3 ...
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126 become zero 3d root arithmetical progression 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 given number 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