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New and Easy Method of Solution of the Cubic and Biquadratic Equations ...
No preview available - 2015
algebraical alternately positive auxiliary cubic equation biquadratic roots Cardan's formula contracted division COROLLARY cube roots cyphers Demonstration.—Let Demonstration.—The developed diminishing the roots divide eight figures equa equal roots equation are real equation b c equation of differences equation whose second equation Y Extract the cube final term four roots fourth degree hence Horner's method multiply the roots number of figures numerical solution ORSON PRATT permanent divisor places of decimals places of figures positive or negative positive root prop proposed equation proposition ratio real roots remaining roots represented Required the roots required to transform right hand figure root figure roots are imaginary roots are real roots imaginary roots of Y second coefficient second term signs changed sixteen figures square root substitute subtract term of formula three figures three imaginary roots three roots Transform the equation trial divisor true divisor unknown quantity
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 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...