Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical ExamplesA. S. Barnes & Burr, 1860 - 400 páginas |
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Página 359
... variations in the signs , that is , in which all the terms are positive , must have all of its real roots negative ; for , every positive number substituted for x , will render the first member essentially positive . Second . 288. Every ...
... variations in the signs , that is , in which all the terms are positive , must have all of its real roots negative ; for , every positive number substituted for x , will render the first member essentially positive . Second . 288. Every ...
Página 362
... variations in the signs of its terms , nor a greater number of negative roots than there are permanences of these signs . A variation is a change of sign in passing along the terms . A permanence is when two consecutive terms have the ...
... variations in the signs of its terms , nor a greater number of negative roots than there are permanences of these signs . A variation is a change of sign in passing along the terms . A permanence is when two consecutive terms have the ...
Página 363
... variation , and in the second , one variation and one permanence . Since in either form , one root is positive and one negative , it fol- lows that there are as many positive roots as there are variations , and as many negative roots as ...
... variation , and in the second , one variation and one permanence . Since in either form , one root is positive and one negative , it fol- lows that there are as many positive roots as there are variations , and as many negative roots as ...
Página 364
... variation which is not found in the proposed equation ; and if , after passing into the lower line , we continue in it throughout , we shall find for the remaining terms the same variations and the same permanences as in the given ...
... variation which is not found in the proposed equation ; and if , after passing into the lower line , we continue in it throughout , we shall find for the remaining terms the same variations and the same permanences as in the given ...
Página 365
... variations of the signs , p the number of permanences ; then , m = n + p . Moreover , let n ' denote the number of positive roots , and p the number of negative roots , we shall have m = n ' + p ' ; whence , n + p = n ' + p ' , or , n ...
... variations of the signs , p the number of permanences ; then , m = n + p . Moreover , let n ' denote the number of positive roots , and p the number of negative roots , we shall have m = n ' + p ' ; whence , n + p = n ' + p ' , or , n ...
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Términos y frases comunes
algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes called co-efficient contrary signs cube root decimal places deduce denote the number derived polynomial Divide dividend entire number example exponent extract the square figures Find the factors Find the square find the values following RULE formula fourth fractional unit given equation given number gives greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier negative roots nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots remainder required root required to find result second degree second member second term simplest form square root substituted subtract suppose supposition take the equation taken third unknown quantity whence whole number write
Pasajes populares
Página 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Página 290 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 286 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Página 117 - The first ten numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Roots.
Página 136 - Resolve the quantity under the radical sign into two factors, one of which is the greatest perfect power of the same degree as the radical.
Página 200 - RULE I. Separate the given number into periods. of three figures each, beginning at the right hand ; the left hand period will often con tain less than three places of figures.
Página 100 - If A and B together can perform a piece of work in 8 days, A and c together in 9 days, and B and c in 10 days, how many days will it take each person to perform the same work alone.
Página 62 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator. EXAMPLES FOR PRACTICE.
Página 154 - B, departed from different places at the same time, and travelled towards each other. On meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 15| days, but B would have been 28 days in performing A's journey. How far did each travel ? Ans.
Página 222 - Consequently, teueя the index of the radical is divisible by the exponent of the power to which it is to be raised, perform the division, leaving the quantity under the radical sign unchanged.