If `f(x)=(x-1)(x-2)(x-3)(x-4),` then cut of the three roots of `f(x)=0`

If f(x)=(1+x)(1+x^2)(1+x^3)(1+x^4) , then f'(0)=1

if f(x)=(x -4) (x-5) (x-6) (x-7) then, (A) f'(x) =0 has four roots (B) three roots f'(x) =0 lie in (4,5) uu(5,6) uu(6,7) (C) the equation f'(x) =0 has only one real root. (D) three roots of f'(x) =0 lie in (3,4) uu (4,5) uu (5,6)

Let f(x)=(x-4)(x-5)(x-6)(x-7) then.(A) f'(x)=0 has four roots (B)Three roots of f'(x)=0 lie in (4,5)uu(5,6)uu(6,7) (C) The equation f'(x)=0 has only one real root (D) Three roots of f'(x)=0 lie in (3,4)uu(4,5)uu(5,6)

Let f(x) be a polynomial with real coefficients such that f(0)=1 and for all x ,f(x)f(2x^(2))=f(2x^(3)+x) The number of real roots of f(x) is:

Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f'(x) ^(2). Let n be the numbers of real roots of g(x) =0, then:

If f is continuous function at x=0, where f(x)=((2^(x)+3^(x))/(2))^((2)/(x)), then f(0) is one of the roots of the equation

If f(x)=x^(3)-3x+1, then the number of distinct real roots of the equation f(f(x))=0 is

If f(x) is a quadratic expression such that f(1)+f(2)=0, and -1 is a root of f(x)=0, then the other root of f(x)=0 is :