If for `xgt0f(x)=(a-x^n)^(1/n), g(x)=x^2+px+q,p,q epsilon R` and equation `g(x)-x=0` has imaginary roots, then number of real roots of equation `g(g(x))-f(f(x))=0` is
(A) 0
(B) 2
(C) 4
(D) none of these

Sum of roots of equations f(x) - g(x)=0 is (a)0 (b) 2alpha (c) -2alpha (d) 4alpha

Let f(x)=x^2 and g(x)=2^x . Then the solution set of the equation fog(x)=gof(x) is (a)R (b) {0} (c) {0, 2} (d) none of these

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

g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4. Number of real roots of the equation g(x) = 0 is

If p,q,r epsilon R and are distinct the equation (x-p)^5+(x-q)^5+(x-r)^5=0 has (A) four imaginary and one real root (B) two imaginary and three real roots (C) all the roots real (D) none of these

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

If p,q be non zero real numbes and f(x)!=0, x in [0,2] also f(x)gt0 and int_0^1 f(x).(x^2+px+q)dx=int_1^2 f(x).(x^2+px+q)dx=0 then equation x^2+px+q=0 has (A) two imginary roots (B) no root in (0,2) (C) one root in (0,1) and other in (1,2) (D) one root in (-oo,0) and other in (2,oo)

If one root of x^(2) + px+12 = 0 is 4, while the equation x ^(2) + px + q = 0 has equal roots, then the value of q is

If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac !=0, then prove that f(x)g(x)=0 has at least two real roots.

If -4 is a root of the equation x^(2)+px-4=0 and the equation x^(2)+px+q=0 has equal roots, then the value of q is