 | John Radford Young - 1835 - 304 σελίδες
...all be doubtful. For cubic equations, indeed, any such caution is altogether unnecessary, because, as every equation of an odd degree has at least one real root, whose situation in the numerical scale is always discoverable by the method in last chapter, there... | |
 | John Radford Young - 1839 - 332 σελίδες
...if an equation have all its roots impossible, the last term must always be positive. Cor. 4. Hence every equation of an odd degree has at least one real root of a contrary sign to that of the last term ; and every equation of an even degree, whose last term... | |
 | John Radford Young - 1842 - 276 σελίδες
...quantity, the results have the same sign .... ib. .21. This invariable sign is necessarily plus . . .20 22. Every equation of an odd degree has at least one real root, of which the sign is opposite to that of the final term of the equation ....... ib. 23. Every equation... | |
 | William Scott - 1844 - 568 σελίδες
...(+a*)=+"s) ; and Y cannot change its sign, because the equation Y=0 contains only imaginary roots. 262. Every equation of an odd degree has at least one real root of a sign contrary to its last term. The first term being always supposed positive, let, in the first... | |
 | Samuel Alsop - 1848 - 336 σελίδες
...essentially positive, and therefore the absolute number R must be positive. (Art. 136, Cor. 2.) Cor. 3. Every equation of an odd degree has at least one real root of a contrary sign to that of the last term ; and every equation of an even degree, the last term of... | |
 | William Smyth - 1855 - 370 σελίδες
...positive ; hence the absolute term of an equation whose roots are all imaginary must be positive. 3°. Every equation of an odd degree has at least one real...necessarily have a contrary sign to that of the last term. - 4". Every equation of an even degree whose last term is negative has, at least, two real roots ;... | |
 | John Radford Young - 1857 - 324 σελίδες
...if an equation have all its roots impossible, the last term must always be positive. Cor. 4. Hence every equation of an odd degree has at least one real root of a contrary sign to that of the last term; and every equation of an even degree, whose last term... | |
 | William Smyth - 1858 - 344 σελίδες
...positive; hence the absolute term of an equation whose roots are all imaginary must be positive. 3°. Every equation of an odd degree has at least one real...necessarily have a contrary sign to that of the last term. 4°. Every equation of an even degree whose last term is negative has, at least, two real roots; and... | |
 | Jeremiah Day - 1859 - 422 σελίδες
...Ans. 2 and 0. Ex. 4. What is the integral part of a root of the equation x>—x3+'l=Q? »»•"»!. Every equation of an odd degree has at least one real root, of a different sign from that of its last term. Let the equation be —3 . . . ± E/=0. And first,... | |
 | Charles Hutton - 1860 - 1020 σελίδες
...and, therefore, the absolute term of an equation whose roots are all impossible must be positive. Cor. 4. Every equation of an odd degree has at least one real root, and that root must, necessarily, bave a contrary sign to that of the last term. Cor. 5. Every equation... | |
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Every equation of an odd degree has at least one real root ; and if there be but one, that root must necessarily have a contrary sign to that of the last term. - 4". 
