Let `f(x) = x^2 + ax + b` , where `a,b in R` . If `f (x)=0` has all its roots imaginary then the roots of `f(x)+ f'(x)+f"(x)=0` are

Let f(x)=ax^(2)+bx+c, where a,b,c,in R and a!=0, If f(2)=3f(1) and 3 is a roots of the equation f(x)=0, then the other roots of f(x)=0 is

Let f(x) = ax^(2) + bx + c, a, b, c, in R and equation f(x) - x = 0 has imaginary roots alpha, beta . If r, s be the roots of f(f(x)) - x = 0 , then |(2,alpha,delta),(beta,0,alpha),(gamma,beta,1)| is

Let f(x) =ax^(2) -b|x| , where a and b are constants. Then at x = 0, f (x) is

Let f(x)=ax^(5)+bx^(4)+cx^(3)+dx^(2)+ ex , where a,b,c,d,e in R and f(x)=0 has a positive root. alpha . Then,

Let f(x)=ax^(2)-b|x| , where a and b are constant . Then at x=0 , f(x) has

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

Two distinct polynomials f(x) and g(x) defined as defined as follow : f(x) =x^(2) +ax+2,g(x) =x^(2) +2x+a if the equations f(x) =0 and g(x) =0 have a common root then the sum of roots of the equation f(x) +g(x) =0 is -

Let a in R and f : R rarr R be given by f(x)=x^(5)-5x+a , then (a) f(x)=0 has three real roots if a gt 4 (b) f(x)=0 has only one real root if a gt 4 (c) f(x)=0 has three real roots if a lt -4 (d) f(x)=0 has three real roots if -4 lt a lt 4