An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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... Equal Roots . III . Real Roots . , 186 186 195 a 10 201 Ap 201 210 the en 214 el CHAPTER IX . CONTINUED FRACTIONS . 248 EXPONENTIAL EQUATIONS AND LOGARITHMS . SECTION I. Exponential Equations . 263 II . Nature and Properties of ...
... Equal Roots . III . Real Roots . , 186 186 195 a 10 201 Ap 201 210 the en 214 el CHAPTER IX . CONTINUED FRACTIONS . 248 EXPONENTIAL EQUATIONS AND LOGARITHMS . SECTION I. Exponential Equations . 263 II . Nature and Properties of ...
Page 123
... root nearly equal to 3. Solve the equation 132 , 6 . Ans . -5-87205266 . x4 + 8 x2 + 16 x = 440 , which has two roots , the first being nearly 4 and the second nearly -4 . 4. Solve the equation Ans . 3-97601 and 2 x4 - 20 x = - 19 , 4 ...
... root nearly equal to 3. Solve the equation 132 , 6 . Ans . -5-87205266 . x4 + 8 x2 + 16 x = 440 , which has two roots , the first being nearly 4 and the second nearly -4 . 4. Solve the equation Ans . 3-97601 and 2 x4 - 20 x = - 19 , 4 ...
Page 201
... root of the equation xn + axn - 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 . or Proof . Denote x - x ... Equal Roots 210.
... root of the equation xn + axn - 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 . or Proof . Denote x - x ... Equal Roots 210.
Page 203
... roots of the equation xn - 1 + a ' xn - 2 + b'xn - 3 + & c . = 0 . If now x " is one of the roots of this last ... equal to each other , and in this case the number of unequal roots is less than the degree of the equation . 1 ...
... roots of the equation xn - 1 + a ' xn - 2 + b'xn - 3 + & c . = 0 . If now x " is one of the roots of this last ... equal to each other , and in this case the number of unequal roots is less than the degree of the equation . 1 ...
Page 204
... roots , one equal to , 7 , three equal to -4 , and five equal to 1 . 271. Corollary . The equation xn a would appear to have but one root , that is , 71 X Να ; but it must , by art . 269 , have n roots , or rather , the nth root of a ...
... roots , one equal to , 7 , three equal to -4 , and five equal to 1 . 271. Corollary . The equation xn a would appear to have but one root , that is , 71 X Να ; but it must , by art . 269 , have n roots , or rather , the nth root of a ...
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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