Theory of Quadratics. 



73 



whence 



and 



Therefore 



a-\-b=~c 



2ab=^2f. 

 I . I 



Find the vahie of " -f f in terms of e and f. 

 a b -' 



a-\-b f 



a b 



ab 



3- 

 4- 



Prove (a — by=(^~/\^f. 



Find the value of r+ ~in terms of e and f. 

 b a 



5. Given the equation x" + ex +/= o, form the equation whose 

 roots are the squares of the roots of this equation. 



If the roots of this equation be called a and b, the roots of the 

 required equation will be a" and b\ The coefficient of x must 

 then be «" + /^" 



or, by Ex. i, ^—2/. 



The absolute term must be a'b" 

 or /^ 



Hence the required equation must be 



6. Form an equation whose roots shall be the reciprocals of 

 the roots of :r^+^.r-f/=o. 



7. Prove that the equation x^—kx—d^=o cannot have im- 

 aginary roots. 



8. Find the value of 7n such that the roots oi x^-\-ex-\-7n—o 

 will differ by 2. 



A— 9 



