An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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... Roots . III . Real Roots . on 201 he 201 en · 210 214 el CO CHAPTER IX . W CONTINUED FRACTIONS . 248 EXPONENTIAL EQUATIONS AND LOGARITHMS . SECTION I. Exponential Equations . • II . Nature and Properties of Logarithms . III . Common ...
... Roots . III . Real Roots . on 201 he 201 en · 210 214 el CO CHAPTER IX . W CONTINUED FRACTIONS . 248 EXPONENTIAL EQUATIONS AND LOGARITHMS . SECTION I. Exponential Equations . • II . Nature and Properties of Logarithms . III . Common ...
Page 201
... root of the equation x2 + a x n - 1 + bxn − 2 + & c . + m = 0 is denoted by x ' , the first member of this equation is a polynomial , divisible by x - x ' , without regard to the value of x . Proof . Denote x - x ' by ... Roots Real Roots.
... root of the equation x2 + a x n - 1 + bxn − 2 + & c . + m = 0 is denoted by x ' , the first member of this equation is a polynomial , divisible by x - x ' , without regard to the value of x . Proof . Denote x - x ' by ... Roots Real Roots.
Page 203
... roots of the equation -1 - xn − 1 + a ' xn − 2 + b'xn - 3 + & c . = 0 . If now x " is one of the roots of this ... real or rational ; they may , on the contrary , be irrational or even imaginary . 270. Scholium . Some of the roots x ...
... roots of the equation -1 - xn − 1 + a ' xn − 2 + b'xn - 3 + & c . = 0 . If now x " is one of the roots of this ... real or rational ; they may , on the contrary , be irrational or even imaginary . 270. Scholium . Some of the roots x ...
Page 213
... roots are , therefore , found from solving the quadratic equation x2 + x - 6 = 0 , X- which gives x = 2 , or == 3 ... Real Roots . Ans . x 1 , CH . VIII . § II . ] 213 1 EQUAL . Roots .
... roots are , therefore , found from solving the quadratic equation x2 + x - 6 = 0 , X- which gives x = 2 , or == 3 ... Real Roots . Ans . x 1 , CH . VIII . § II . ] 213 1 EQUAL . Roots .
Page 214
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Number of Real Roots . Ans . x 1 , or = = 2 . 9. Find all the roots of the equation x5 — 2 x1 — 2 x3 + 4x2 + x - 2 = 0 --- - · which has equal roots . 10. Find all the ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Number of Real Roots . Ans . x 1 , or = = 2 . 9. Find all the roots of the equation x5 — 2 x1 — 2 x3 + 4x2 + x - 2 = 0 --- - · which has equal roots . 10. Find all 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