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" The algebraic sum of the two roots is equal to the coefficient of the second term taken with the contrary sign. "
Elements of Algebra - Page 127
by Bourdon (M., Louis Pierre Marie) - 1831 - 304 pages
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Elements of Algebra: Tr. from the French of M. Bourdon, for the ..., Volume 1

Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 446 pages
...from the two following properties of the equation x3 +px — <7=0, viz. : The algebraic sum of the roots is equal to the coefficient of the second term, taken with a contrary sign, and their product is equal to the last term, or the known term transposed into the...
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Elements of Algebra

William Smyth - Algebra - 1836 - 288 pages
...sum, it is evident, will be — p ; if we multiply them together the product will be — q ; whence 1°. The algebraic sum of the two roots is equal to the coefficient of the. second term, taken with a contrary sign. 2°. The product of the two roots is equal to the second member of the equation, taken...
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Elements of Algebra

Charles Davies - Algebra - 1842 - 368 pages
...equation of the second degree demonstrated in (Art. 143). The properties are : The algebraic, sum of the roots is equal to the co-efficient of the second term, taken with a contrary sign, and their product is equal to the second member, taken also with a contrary sign....
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Elements of Algebra: Including Sturms' Theorem

Charles Davies - Algebra - 1845 - 382 pages
...the roots, we obtain, x' + x" = — 2p ; and by multiplying them together, x'oc" = — q. Hence, 1st. The algebraic sum of the two roots is equal to the co-efficient of the second term of the equation, taken with a contrary sign. 2d. The product of the two roots is equal to the absolute...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...radical parts having opposite signs disappear and we obtain I -P P- „ lz z~ f. Hence, • PROPERTY III. The algebraic sum of the two roots is equal to the coefficient of the second term of the equation, taken with a contrary sign. Thus, in Example 1, page 172, x-~Wx= — 16, the two roots...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 376 pages
...equation я*— 2x— 24=0, are + 6 and — 4. Resolve it into its factors. Hence, PEOPEETY III. ГЛе algebraic sum of the two roots is equal to the coefficient of the second term of the equation, taken with a contrary sign. Thus, in Example 1, page 172, ж2— 10ж= — 16, the...
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Elements of Algebra

William Smyth - 1847 - 276 pages
...sum, it is evident, will be — P ; if we multiply them together the product will be — Q ; whence 1°. The algebraic sum of the two roots is equal to...2°. The product of the two roots is equal to the second member of the equation, taken also with a contrary sign. 116. Let us new proceed to the discussion...
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Elements of Algebra: Including Sturms' Theorem

Algebra - 1848 - 394 pages
...the roots, we obtain, a/ + x" = — 2p ; and by multiplying them together, x'x" = — q. Hence, 1st. The algebraic sum of the two roots is equal to the co-efficient nf the second term of the equation, taken with a contrary sigr 2d. The product of the two roots is...
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Elementary Algebra: For the Use of Schools

William Smyth - Algebra - 1851 - 272 pages
...— q. The roots of an equation of the second degree will have, therefore, the following properties : 1° The algebraic sum of the two roots is equal to the coefficient of x in the second term, taken with a contrary sign. 2°. The product of the roots is equal to the known...
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Treatise on Algebra, for the Use of Schools and Colleges

William Smyth - Algebra - 1855 - 370 pages
...sum, it is evident, will be — P; if we multiply them together the product will be — Q ; whence 1°. The algebraic sum of the two roots is equal to...2°. The product of the two roots is equal to the second member of the equation, taken also with a contrary sign. 116. Let us new proceed to the discussion...
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