An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
From inside the book
Results 6-10 of 16
Page 225
... row of signs when x = ∞ is + , + , ( the reverse of a ) , - ; and when x = — ∞o it is - ,, ( like a ) , — , so that there is only one real root . The row of signs when x = 0 is , when b is positive , + , ( like a ) , — , — , so that ...
... row of signs when x = ∞ is + , + , ( the reverse of a ) , - ; and when x = — ∞o it is - ,, ( like a ) , — , so that there is only one real root . The row of signs when x = 0 is , when b is positive , + , ( like a ) , — , — , so that ...
Page 226
... row of signs when x = ∞o is and that when x = ∞ is + , + , + ; + , - - ; so that the two different roots of the equation are , in this case , real . The row of signs when x = 0 is ( like b ) , — , Ħ ( unlike b ) ; so that one of the ...
... row of signs when x = ∞o is and that when x = ∞ is + , + , + ; + , - - ; so that the two different roots of the equation are , in this case , real . The row of signs when x = 0 is ( like b ) , — , Ħ ( unlike b ) ; so that one of the ...
Page 227
... row of signs when x = ∞ is ; + , + , ( unlike a ) , + ; when x = ∞ it is + ,, ( like a ) , + ; so that when a is positive , there is no real root , and when a is negative there are two real roots . In the latter case , the row of signs ...
... row of signs when x = ∞ is ; + , + , ( unlike a ) , + ; when x = ∞ it is + ,, ( like a ) , + ; so that when a is positive , there is no real root , and when a is negative there are two real roots . In the latter case , the row of signs ...
Page 228
... row of signs when x = ∞ is + , + , when x = 0 it is - ( unlike a ) , — ; + ( like a ) , — ; ? so that when a is negative there is no real root , and when a is positive there are two real roots . In the latter case , the row of signs ...
... row of signs when x = ∞ is + , + , when x = 0 it is - ( unlike a ) , — ; + ( like a ) , — ; ? so that when a is negative there is no real root , and when a is positive there are two real roots . In the latter case , the row of signs ...
Page 229
... row of signs when x = ∞ is when x = ∞ it is ++ , + + ; - --- so that the equation has three real roots ; the row of signs when x = 0 is ± ( like b ) , - , ( unlike b ) , + ; so that when b is negative , one of the real roots is posi ...
... row of signs when x = ∞ is when x = ∞ it is ++ , + + ; - --- so that the equation has three real roots ; the row of signs when x = 0 is ± ( like b ) , - , ( unlike b ) , + ; so that when b is negative , one of the real roots is posi ...
Other editions - View all
Common terms and phrases
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