 | Mathematics - 1823 - 272 pages
...+ q be the three roots ; then, by the property of equations, the sum of the roots of every equation is equal to the co-efficient of the second term with its sign changed, and the sum of the product of every two is equal to the co-efficient of the third term without any change in... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 446 pages
...would result 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... | |
 | Peter Nicholson - Algebra - 1831 - 326 pages
...3=4 or — 10. Or, the value of the unknown quantity, in any equation, may be found, by taking half the coefficient of the second term, with its sign changed, and + the square root of the square of the half coefficient added to the known quantity. For by taking the above... | |
 | Charles Davies - Algebra - 1835 - 378 pages
...of an 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 wth a contrary sign, and their product is equal to the second member, taken also with a contrary... | |
 | Algebra - 1838 - 372 pages
...of an 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 thiir product is equal to the second member, taken also with a contrary... | |
 | Thomas Grainger Hall - 1840 - 266 pages
...respectively represent these two values; «— Therefore, a + ß = — p, or the sum of the values of л; is equal to the coefficient of the second term with its sign changed : this proposition is true of equations of any dimensions whatever. Again, «/3=CHence, if we write... | |
 | Charles Davies - Algebra - 1842 - 368 pages
...of an 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... | |
 | Charles Davies - Algebra - 1845 - 382 pages
...two properties of an equation of the second degree, demonstrated in Art. 143. They 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 absolute term, taken also with a contrary... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 474 pages
...also the sum of lite two roots of a quadratic equation of the form x* + ax + b = 0 is equal to — a, the coefficient of the second term with its sign changed, and the product of the two roots is equal to b, the last term. For if r and r' be the two roots of the equation x* + ax +... | |
 | Euclid - Geometry - 1853 - 176 pages
...is identical with the equation and therefore a geometrical proof of the second theorem that the snm of the roots is equal to the coefficient of the second term. Again, in the geometrical demonstration of the second case of the problem, it is shown that the rectangle... | |
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... the sum of the roots is equal to the coefficient of the second term with its sign changed, and the product of the roots is equal to the last term. 
