 | Bourdon (M., Louis Pierre Marie) - 1831 - 446 σελίδες
...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... | |
 | William Smyth - 1836 - 288 σελίδες
...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... | |
 | Charles Davies - 1842 - 368 σελίδες
...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.... | |
 | Charles Davies - 1845 - 382 σελίδες
...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... | |
 | Elias Loomis - 1846 - 380 σελίδες
...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... | |
 | Elias Loomis - 1846 - 376 σελίδες
...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... | |
 | William Smyth - 1847 - 276 σελίδες
...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... | |
 | 1848 - 394 σελίδες
...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... | |
 | William Smyth - 1851 - 272 σελίδες
...— 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... | |
 | William Smyth - 1855 - 370 σελίδες
...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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The algebraic sum of the two roots is equal to the coefficient of the second term taken with the contrary sign. 
