 Therefore, in the third and fourth forms, when q is greater than p2, that is, when the known term is negative, and greater than the square of half the coefficient of the first power of x, both values of the unknown quantity are impossible.  Elements of Algebra - Page 112by Silvestre François Lacroix - 1825 - 276 pagesFull view - About this book
 | 1867 - 878 pages
...the first term. From this principle is derived the following METHOD FOB COMPLETING THE SQUARE. Take the square of half the co-efficient of the first power of the unknown quantity, and add it to both tides of the equation. It will be observed that there is nothing peculiar in the... | |
 | William Nicholson - 1809 - 716 pages
...all the terms, that the equation may be reduced to this farm, x* ^ px = i J. Then add to both sides the square of half the co-efficient of the first power of the unkwown quantity, by which means the first side of the equation is made a complete square, and the... | |
 | Adrien Marie Legendre - 1819 - 574 pages
...when q exceeds ?-. It will be perceived then from what has been said, how, and for what reason, when the known term of an equation of the second degree...greater than the square of half the coefficient of thcJirst power of the unknown quantity, tins equation can have only imaginary roots. 115. The expressions... | |
 | William Nicholson - 1819 - 432 pages
...all the terms, that the equation may be reduced to this form, x' ±px = ± g. Then add to both sides the square of half the co-efficient of the first power of the unknown quantity, by which means the first side 6f the equation is made a complete square, and the other consists of... | |
 | Jeremiah Day - 1820 - 352 pages
...derived the following rule : 305. To COMPLETE THE SQUARE, in an affected quadratic equation ; TAKE THE SQUARE OF HALF THE CO-EFFICIENT OF THE FIRST POWER OF THE UNKNOWN QUANTITY, AND ADD IT TO. BOTH SIDES OF THE EQUATION. Before completing the square, the known and unknown quantities... | |
 | 1821 - 526 pages
...of the question, the necessity of the roots being imaginary in an equation, of which the known term is negative in the second member, and greater than...coefficient of the first power of the unknown quantity, he gives a striking specimen of his way of investigating ' analytical facts,' and displaying the spirit... | |
 | Adrien Marie Legendre - 1825 - 570 pages
...when l{ exceeds—. It will be perceived then from what has been said, how, and for what reason, when the known term of an equation of the second degree...quantity, this equation can have only imaginary roots. 115. The expressions > V'"^, a + \s~-bi and, in general, those, which involve the square root of a... | |
 | Jeremiah Day - 1827 - 352 pages
...is derived the following rule: 305. To COMPLETE THE SQUARE, in an affected quadratic equation ; TAKE THE SQUARE OF HALF THE CO-EFFICIENT OF THE FIRST POWER OF THE UNKNOWN QUANTITY, AND ADD IT TO BOTH SIDES OF THE EQUATION. Before completing the square, the known and unknown quantities... | |
 | 1836 - 488 pages
...square of that quantity in another term. To complete the square of an affected quadratic equation, take the square of half the co-efficient of the first power of the unknown quantity, and add it to both sides of the equation. After the square is completed, the equation is reduced, by... | |
 | James Bates Thomson - 1844 - 266 pages
...first term. 257. From this principle is derived the following METHOD FOR COMPLETING THE SQUARE. Take the square of half the co-efficient of the first power of the unknown quantity, and add it to both sides of the equation. 258. It will be observed that there is nothing peculiar in... | |
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