New and Easy Method of Solution of the Cubic and Biquadratic Equations: Embracing Several New Formulas, Greatly Simplifying this Department of Mathematical Science

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Longmans, Green, Reader, and Dyer, 1866 - Equations - 151 pages
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Page 1 - An equation in which the highest power of the unknown quantity is of the second degree, that is, a square, is called an equation of the second degree, or a quadratic equation.
Page 2 - An equation of the second degree is one in which the highest power of the unknown quantity is the second power, or square ; as, 3 ж2 — 2 x — 65.
Page 19 - Any equation may be transformed into another, the roots of which shall be greater or less than those of the former by a given quantity.
Page 14 - Hence, if the coefficient of the second term in any equation be 0 ; that is, if the term be absent, the sum of the roots...
Page 136 - If the coefficient of the second term in any equation is 0, that is, if the second term is wanting, the sum of the positive roots is equal to the sum of the negative roots.
Page 17 - ... its degree, that is, when no coefficient is zero. And we shall sometimes find it useful to render an equation complete by the artifice used above, that is, by introducing the missing terms with zero for the coefficient of each of them. 52. To transform an equation into another the roots of which are equal to those of the proposed equation multiplied by a given quantity. Let f(x) = 0 denote the proposed equation ; and let it be required to transform it into another the roots of which are k times...

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