If for all real values of a one root of the equation `x^2-3ax + f(a)=0` is double of the other, then f(x) is equal to

If one root of equation x^(2)-4ax+a+f(a)=0 is three times of the other then minimum value of f(a) is

If one the roots fo the equation x^(2) +x f(a) + a=0 is the cube of the othere for all x in R , then f(x)=

If one the roots fo the equation x^(2) +x f(a) + a=0 is the cube of the othere for all x in R , then f(x)=

If one root of the equation (a-b) x^(2)+a x+1=0 is double the other and if a is real, then the greatest value of b is

One root of the equation ax^(2)-3x+1=0 is (2+i) . Find the value of 'a' when a is not real.

If one of the roots of the quadratic equation,x^(2)-xf(t)+t=0 is equal to the third power of the other.If f is a real valued function.The set of all values of t for which f is defined will be

Let f((x+y)/2) = (f(x)+f(y))/2 for all real values of x and y. If f^(')(0) exists and equals -1 and f(0) =1, then f^(')(2) is equal to

If one root of the quadratic equation (a-b)x^(2)+ax+1=0 is double the other root where a in R, then the greatest value of b is