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

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Page 203

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**real**or rational ; they may , on the contrary , be irrational or even imaginary . 270. Scholium . Some of the roots x ' , x ' ' , x ' ' ' , & c . , are often equal to each other , and in this case the**number**of unequal roots is less ... Page 214

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

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 ... Page 215

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

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 , and this number is ... Page 216

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

**Number of Real**Roots between two given Numbers . value of Y by Y ' ; and when we substitute q for X , and de- note the corresponding value of Y by Y " , it becomes ...### 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