 If each negative coefficient be taken positively and divided by the sum of all the positive coefficients which precede it, the greatest of all the fractions thus formed increased by unity, is a superior limit of lhe positive roots. Let the equation be...  First Course in the Theory of Equations - Page 22by Leonard Eugene Dickson - 1922 - 168 pagesFull view - About this book
 | John Hymers - Algebra - 1811 - 230 pages
...Here r =* 3, and a limit of the positive roots ^44. If each negative coefficient, taken positively, be divided by the sum of all the positive coefficients which precede it, the greatest of the fractions thus formed, increased by unity, is a superior limit of the positive roots. Let the... | |
 | John Radford Young - Equations - 1842 - 276 pages
...A,x'. Hence if fractions be formed by taking each negative coefficient positively, and dividing it by the sum of all the positive coefficients which precede it, the greatest of these fractions Increased by unity will exceed the greatest positive root of the equation. (48.)... | |
 | Bengal council of educ - 1848 - 394 pages
...standard form they can all be reduced. 4. In any equation if each negative coefficient taken positively be divided by the sum of all the positive coefficients which precede it, the greatest of the fractions thus formed increased by unity is a superior limit of the positive roots. SCHOLARSHIP... | |
 | Education - 1851 - 626 pages
...standard form they can all be reduced. 4. In any equation if each negative coefficient taken positively be divided by the sum of all the positive coefficients which precede it, the greatest of the fractions thus formed increased by unity is a superior limit of the positive roots. XXX 6. In... | |
 | Isaac Todhunter - Equations, Theory of - 1861 - 330 pages
...the positive roots of the equation f(x) = 0. 90. If each negative coefficient be taken positively and divided by the sum of all the positive coefficients which precede it, the greatest of all the fractions thus formed increased by unity, is a superior limit of the positive roots. Let... | |
 | Isaac Todhunter - Algebra - 1875 - 344 pages
...positive roots of the equation f(x) = 0. 90. Jf each negative coefficient lie taken positively and divided by the sum of all the positive coefficients which precede it, tlte greatest of all tJie fractions thus formed increased by unity, is a superior limit of the positive... | |
 | William Snow Burnside, Arthur William Panton - Determinants - 1881 - 407 pages
...+\/pk. 79. Proposition II. — If in any equation' each negative coefficient be taken positively, and divided by the sum of all the positive coefficients which precede it, the greatest quotient thus formed increased by unity is a superior limit of the positive roots. Let the equation be a 0 at... | |
 | William Snow Burnside, Arthur William Panton - Determinants - 1886 - 474 pages
...+Vjp*79. Proposition II. — If in any equation each negative coefficient be taken positively, and divided by the sum of all the positive coefficients which precede it, the greatest quotient thus formed increased by unity is a superior limit of the positive roots. Let the equation be floit"... | |
 | William Snow Burnside, Arthur William Panton - Determinants - 1886 - 480 pages
...+\/pk79. Proposition II. — If in any equation each negative coefficient be taken positively, and divided by the sum of all the positive coefficients which precede it, the greatest quotient thus formed increased by unity is a superior limit of the positive roots. Let the equation be Ootf"... | |
 | Isaac Todhunter - Equations, Theory of - 1904 - 344 pages
...the positive roots of the equation f(x) = 0. 90. If each negative coefficient be taken positively and divided by the sum of all the positive coefficients which precede it, the greatest of all the fractions thus formed increased by unity, is a superior limit of lhe positive roots. Let... | |
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