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" ... 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. "
Elements of Geometry - Page 122
by Adrien Marie Legendre - 1825 - 224 pages
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Elements of Algebra

Silvestre François Lacroix - Algebra - 1833 - 320 pages
...when those of y would be so, they become therefore imaginary in the case under consideration, when q exceeds ^-. It will be perceived then from what has...can have only imaginary roots. 115. The expressions quantity, are called imaginary quantities.* They are mere symbols of absurdity, that take the place...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 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...
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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

James Bates Thomson - Algebra - 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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Elements of Algebra: Embracing ... the Theory and Application of Logarithms ...

Davis Wasgatt Clark - 1844 - 394 pages
...first, second, third, or fourth power, the first member may be rendered a perfect square by adding the square of half the coefficient of the first power of the unknown quantity to both members of the equation. This is called completing the square. 326. Each of the above equations...
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Elements of Algebra: Embracing Also the Theory and Application of Logarithms ...

Davis Wasgatt Clark - Algebra - 1846 - 374 pages
...first, second, third, or fourth power, the first member may be rendered a perfect square by adding the square of half the coefficient of the first power of the unknown quantity to both members of the equation. This is called completing the square. 326. Each of the above equations...
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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 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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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 250 pages
...in the third and fourth forms, when q is greater than jf, 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. What is the cause of this impossibility ? To...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 408 pages
...impossible (Art. 193). Hence, when q is greater than p-, that is, when the known term is negative, and greater than the square of half the coefficient of the first power of x, Ote roots are imaginary. To show why the roots are imaginary, we must inquire, into what two parts...
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Ohio Educational Monthly and the National Teacher, Volumes 1-2

Education - 1852 - 844 pages
...rule for completing the square after arranging the terms, is to add to both members of the equation the square of half the coefficient of the first power of the unknown quantity. Bonnycastle, Day, and others, add the following rule for particular cases : Multiply the equation into...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 250 pages
...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. What is the cause of this impossibility ? To...
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