Some Important Result For the quadratic equation ax^2 + bx+c =0 One Root will be reciprocal of other is a=c One root is 0 if c=0 Roots are equal in magnitude but opposite in sign if b=0. Both roots are zero if b=c=0. Roots are positive if a and c are of same sign and b is of the opposite sign Roots are opposite sign if a and c are of opposite signs. Roots are negative if a,b,c are of same sign Let f(x)= ax^2 + bx+c, where a>0.Then Conditions for both the roots of f(x)=0 to be greater than a given number k are b^2 - 4ac >= 0; f(k)=0; -b/2a > k. Conditions for both the roots of f(x)=0 to be less than a given number k are b^2 - 4ac >= 0; f(k)>0; -b/2a < k. The number k lies between the roots of f(x)=0, if b^2 - 4ac > 0; f(k)<0. Conditions for exactly one root of f(x)=0 to be lie between k1, k2 is f(k1)(k2)<0,b^2 - 4ac > 0. Conditions for both roots of f(x)=0 confined between k1, k2 is f(k1)>0, f(k2)>0, b^2 - 4ac >= 0...
