QUADRATIC EQjTATIONS. ' 35^ 



An AFFEC^TED QIJADRATIC EQUATION is that, wllich In- 



vclves the square. of the unknown quantity, together with 

 the product, that arises from multiplying it hy some known 

 quantity. 



Thus, n>:':^b is a simple quadratic equation, 



And ax''-\-lxzzc is an affected quadratic equation. 



The rule for a simple quadratic equation has been given 

 already. 



All affected quadratic equations fail under the three 

 folld'^^ing forms. 



1. X^-\-aX:=zh 



2. r/^ riX-=:h 



3. X' — J/.v=: — b. 



The rule for finding the value of /V, in each of these 

 equations, is as follows : 



Ji u L E,* 



I. Transpose all the terms, that involve t\\Q unknown 

 quantity, to one side of the equation, and the known terms 

 to the other side, and let them be ranged according to 

 (heir dimensions. 



2. When 



* The square root of any quantity may be elt-her -f- or — , 



and therefore all quadratic equations admit of two solutions. 

 Thus, the square root of ■\-n'^ is -j-«> or — n ; for either -f-'^X 

 ^n, or — nx — n is equal to -\-n'^. So in the first form, where 



ff 4" — ^s found ^-y/ ^4" — >the root maybeeithcr -f v' ^~l~ 



2 A 4 



or — ^/ b-^- , since either of them being multiplied by itself 



4 



will produce b-{- — . An' ^^^■'-"-.^■'■•■■""*: expressed by v^•nti^igthe 

 4 



uocertain sign +^ before ^^ i-f- — ; thus a'= + y' b-^ ~~ — f 



2 

 In 



