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 - Side 122av Silvestre François Lacroix - 1825 - 276 siderUten tilgangsbegrensning - Om denne boken
| Popular educator - 1767
...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
...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 - 208 sider
...y would be so, they become therefore imaginary in the case under consideration, when q exceeds ?-. **It will be perceived then from what has been said,...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
...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 - 332 sider
...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... | |
| Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1821
...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 - 224 sider
...y would be so, they become therefore imaginary in the case under consideration, when l{ exceeds—. **It will be perceived then from what has been said,...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 - 332 sider
...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 - 472 sider
...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... | |
| Jeremiah Day, James Bates Thomson - 1844 - 252 sider
...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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