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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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The Complete Algebra: Embracing Simple and Quadratic Equations, Proportion ...

Edward Olney - Algebra - 1877 - 466 pages
...of ±хг — \x + 20£ = 42f, and verify. Roots, 1, and — 6£. SCH. 1. — This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQT.MRE. There...
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The Complete Algebra: Embracing Simple and Quadratic Equations, Proportion ...

Edward Olney - Algebra - 1878 - 516 pages
...roots of Jr« — \x + 20i = 42f, and verify. Roofs, 7, and — 6£. SCH. 1. — This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE. There are...
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A University Algebra

Edward Olney - 1878 - 360 pages
...unknown quantity, its value is found by transposing the second term. SCH. 1. — This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE. There are...
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New Elementary Algebra: Designed for Common and High Schools and Academies

Shelton Palmer Sanford - Algebra - 1879 - 348 pages
...the known quantities on the other. III. Complete the square by adding to both sides of the equation the square of half the coefficient of the first power of the unknown quantity. IV. Extract the square root of both sides, and reduce the resulting equation. NOTE. — It must be...
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Elementary algebra: with brief notices of its history

Robert Potts - Algebra - 1879 - 672 pages
...expressed : — " To the number multiplied by the coefficient of the sqiiare of the unknown quantity, add the square of half the coefficient of the first power of the unknown quantity ; the square root of the sum less half the coefficient of the unknown quantity being divided by the...
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Elementary algebra, with brief notices of its history

Robert Potts - 1879 - 668 pages
...pression), the equation assumes the form ±z=±i1, which gives four equalities : complete square, is the square of half the coefficient of the first power of the unknown quantity, and з?±рх-\- — is a complete square. By means of this property a complete quadratic equation...
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A University Algebra

Edward Olney - Algebra - 1880 - 354 pages
...unknown quantity, its value is found by transposing the second term. SCH. I. — This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQDAKE. There are...
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The Complete Algebra ...

Edward Olney - Algebra - 1881 - 504 pages
...the roots of %х>— \х + Щ = Щ, and verify. 7, and — 6-J-. Scholium. — This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE. There are...
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A University Algebra: Comprising a Compendious, Yet Complete and Thorough ...

Edward Olney - Algebra - 1882 - 358 pages
...unknown quantity, its value is found by transposing the second term. 8сн. 1. — This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE. There are...
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Algebra for the Use of High Schools, Academies and Colleges

John Bernard Clarke - Algebra - 1889 - 566 pages
...If the second member (q) of an equation of the second degree be negative, it cannot be numerically greater than the square of half the coefficient of the first power of the unknown quantity, if the roots be real. p-\-d= the greater quantity, and p—d the less. If q represent their product,...
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