 | 1867 - 878 σελίδες
...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... | |
 | John Mole - 1788 - 346 σελίδες
...Queftion, CAS g CASE VI. When an Equation is prepared for completing the Square if the known Term be negative, and greater than the Square of half the Co-efficient of the fecond Term, then the Roots will be imaginary or impoffible : for EXAMPLE 1 Suppofe *•* — 6ax—... | |
 | William Nicholson - 1809 - 716 σελίδες
...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... | |
 | William Nicholson - 1819 - 432 σελίδες
...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 σελίδες
...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 σελίδες
...the roots being imaginary in an equation, of which the known term is negative in the second member, and greater than the square of half the 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 σελίδες
...what reason, when the known term of an equation of the second degree is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots. 115. The expressions > V'"^, a + \s~-bi and, in general,... | |
 | Silvestre François Lacroix - 1825 - 294 σελίδες
...what reason, when the known term of an equation of the second degree is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots. 1 1 5. The expressions and, in general, those, which involve... | |
 | Jeremiah Day - 1827 - 352 σελίδες
...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 σελίδες
...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... | |
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If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other. 
