 The sum of the roots of a quadratic equation in x is equal to the coefficient of x with its sign changed, divided by the coefficient ofx2.  Notes on algebra - Page 41by Howard Candler - 1885Full view - About this book
 | Louis Parker Jocelyn - Algebra - 1902 - 460 pages
...equation may be shown as follows : Let Аз? + Bx + 0 = 0, or Then 1. The »um of the roots is equal to the coefficient of x, with its sign changed, divided by the coefficient of ж2, В or--- 2. The product of the roots is equal to the known term (7 divided by the coefficient... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1904 - 462 pages
...straight line. QED Corollary I. The slope of the line Ax + Tiij + С = 0 A is m = — — ; that is, the coefficient of x with its sign changed divided by the coefficient of y. Corollary П. The lines Ax + By + С = 0 and A'x + B'y + C' = Q are parallel when and only when... | |
 | Walter Randall Marsh - Algebra - 1905 - 446 pages
...+ ß = -p, (3) multiplying (1) and (2), aß = q. (4) Hence, in the equation ж2 + px + q = 0 : (1) The sum of the roots equals the coefficient of x with its sign changed. (2) The product of the roots equals the absolute term. 231. Since the equation x2 + px + q=Q is the... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - Algebra - 1907 - 304 pages
...+ /3 = -p, (3) multiplying (1) and (2), aß = q. (4) Hence, in the equation ж2 + pж + q = 0: (1) The sum of the roots equals the coefficient of x with its sign changed. (2) The product of the roots equals the absolute term. 52. Since the equation а? + px + q=0 is the... | |
 | William Ernst Paterson - Algebra - 1908 - 614 pages
...of ; 149. The sum of the roots of any quadratic equation is equal to the coefficient of ,< with the sign changed, divided by the coefficient of x2 ; and the product of the roots is equal to the constant term divided by the coefficient of x2. Method I. Consider the standard form... | |
 | Henry Lewis Rietz, Arthur Robert Crathorne - Algebra - 1909 - 292 pages
...ii I — — — . 2a ja Hence : I. Tfie sum, of the roots of a quadratic equation in x is equal to the coefficient of x with its sign changed, divided by the coefficient of я?. II. The product of the roots of a quadratic equation in x is equal to the known term divided by... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1912 - 364 pages
...of (3) is a straight line. QED Corollary. The slope of the line Ax + By + С = 0 is m = ; that is, the coefficient of x with its sign changed divided by the coefficient of y. 26. Plotting straight lines. If the line does not pass through the origin (constant term not zero,... | |
 | Frederick Howland Somerville - Algebra - 1913 - 458 pages
...nrt=-- Hence, we may state : 319. In any affected quadratic equation of the form *2 + -*+- = 0, aa (a) The sum of the roots equals the coefficient of x with its sign changed. (6) The product of the roots is equal to the constant term. Illustrations : 1. Find by inspection the... | |
 | Henry Lewis Rietz, Arthur Robert Crathorne - Algebra - 1919 - 300 pages
...V62 — 4 ac\ _ c — ~ " Hence : I. The sum of the roots of a quadratic equation in x is equal to the coefficient of x with its sign changed, divided by the coefficient ofx*. II. The product of the roots of a quadratic equation in x is equal to the known term divided... | |
 | Arthur McCracken Harding, George Walker Mullins - Geometry, Analytic - 1924 - 346 pages
...aс) = 4_aс = c. 4 a2 4 a2 a Hence (1) the sum of the roots of any quadratic equation is equal to the coefficient of x with its sign changed, divided by the coefficient of x2 ; (2) the product of the roots of any quadratic equation is equal to the constant term divided by the... | |
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