## An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |

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... Roots . III .

... Roots . III .

**Real Roots**. , 186 186 195 a or 201 p the 201 en 210 214 el CHAPTER IX . CONTINUED FRACTIONS . CO ti W 248 EXPONENTIAL EQUATIONS AND LOGARITHMS . SECTION I. Exponential Equations . 263 II . Nature and Properties of ... Page 203

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**roots**of the equation xn - 1 + α ' χη - 2 + b'xn - 3 + & c . = 0 . If now x " is one of the**roots**of this last ...**real**or rational ; they may , on the contrary , be irrational or even imaginary . 270. Scholium . Some of the**roots**... Page 214

To which are Added Exponential Equations and Logarithms Benjamin Peirce. Number of

To which are Added Exponential Equations and Logarithms Benjamin Peirce. Number of

**Real Roots**. 9. Find all the roots of the equation 225 2 x4 - 2 x3 + 4 x2 + x - 2 = 0 which has equal roots . Ans . x = ± 1 , or = 2 . 10. Find all the roots ... Page 215

To which are Added Exponential Equations and Logarithms Benjamin Peirce. Number of

To which are Added Exponential Equations and Logarithms Benjamin Peirce. Number of

**Real Roots**between two given Numbers . that is , there must be a number which , substituted in the first member , reduces it to zero ...**REAL ROOTS**.### Other editions - View all

### Common terms and phrases

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