Page:Elementary algebra (1896).djvu/253

235 Rh CHAPTER XXVI.

Quadratic Equations.

281. Suppose the following problem were proposed for solution:

A dealer bought a number of horses for $280. If he had bought four less, each would have cost $8 more ; how many did he buy ?

We should proceed thus : Let x = the number of horses ; then {x}{280} = the number of dollars each cost.

If he had bought 4 less, he would have had x — 4, horses, and each would have cost {280}{x - 4} dollars. 8 + {x}{280} + {280}{x - 4} whence x(x — 4) + 35(x — 4) = 35 x ; x^2 - 4x + 35x -140 = 35 x; x^2 - 4x = 140.

This equation involves the square of the unknown quantity; and in order to complete the solution of the problem we must discover a method of solving such equations.

282. Definition. An equation which contains the square of the unknown quantity, but no higher power, is called a quadratic equation, or an equation of the second degree.

If the equation contains both the square and the first power of the unknown, it is called an affected quadratic; if it