An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 124
... figure of the root is b places from the decimal point , that of the power must be as many as b times n places from this point , and less than b + 1 times n places from it ; which , combined with the preceding articles , gives the ...
... figure of the root is b places from the decimal point , that of the power must be as many as b times n places from this point , and less than b + 1 times n places from it ; which , combined with the preceding articles , gives the ...
Page 125
... Ans . 8004 . Ans . 806.5 . * This figure must , in the present case , be found by trial , because the first quotient is so inaccurate . Roots of Fractions . Ans . 10.01 . Ans . 11 * CH . IV . § III . ] 125 NUMERICAL EQUATIONS .
... Ans . 8004 . Ans . 806.5 . * This figure must , in the present case , be found by trial , because the first quotient is so inaccurate . Roots of Fractions . Ans . 10.01 . Ans . 11 * CH . IV . § III . ] 125 NUMERICAL EQUATIONS .
Page 127
... figure , di- vided by the divisor , is the next figure of the required root ; which figure is also to be placed at the right of the divisor . Multiply the divisor , thus augmented , by the last figure of the root , subtract the product ...
... figure , di- vided by the divisor , is the next figure of the required root ; which figure is also to be placed at the right of the divisor . Multiply the divisor , thus augmented , by the last figure of the root , subtract the product ...
Page 238
... figure . 309. EXAMPLES . 1. Find the left hand significant figure of the real roots of the equation Solution . 5x36x + 2 = 0 . First . In this case , 6 is the greatest negative coefficient and 6 x is the first negative term , so that ...
... figure . 309. EXAMPLES . 1. Find the left hand significant figure of the real roots of the equation Solution . 5x36x + 2 = 0 . First . In this case , 6 is the greatest negative coefficient and 6 x is the first negative term , so that ...
Page 240
... figures of the roots of the equation x2 + 8 x2 + 16 x 440 0 . Ans . 3 and 4 . - 3. Find the first approximation to the roots of the equa- tion 25-15 x3 132x2 + 36x + 396 0 . Ans . 1 , -1 , - 5 . 4. Find , by Stern's theorem , the ...
... figures of the roots of the equation x2 + 8 x2 + 16 x 440 0 . Ans . 3 and 4 . - 3. Find the first approximation to the roots of the equa- tion 25-15 x3 132x2 + 36x + 396 0 . Ans . 1 , -1 , - 5 . 4. Find , by Stern's theorem , the ...
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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