Show that there exists no polynomial `f(x)` with integral coefficients which satisfy `f(a)=b ,f(b)=c ,f(c)=a ,` where `a , b , c ,` are distinct integers.

Let f(x) be a polynomial with integral coefficients. If f(1) and f(2) both are odd integers, prove that f(x) = 0 can' t have any integral root.

If f(x) is a polynomial of degree four with leading coefficient one satisfying f(1)=1, f(2)=2,f(3)=3 .then [(f(-1)+f(5))/(f(0)+f(4))]

The polynomial f(x)=x^4+a x^3+b x^2+c x+d has real coefficients and f(2i)=f(2+i)=0. Find the value of (a+b+c+d)dot

The polynomial f(x)=x^4+a x^3+b x^2+c x+d has real coefficients and f(2i)=f(2+i)=0. Find the value of (a+b+c+d)dot

f(x) is polynomial of degree 4 with real coefficients such that f(x)=0 satisfied by x=1, 2, 3 only then f'(1) f'(2) f'(3) is equal to -

Let f(x) be a polynomial function of second degree. If f(1) = f(-1) and a, b. c are in A.P., then f'(a), f'(b),f'(c) are in

Let f(x) = x^4 + ax^3 + bx^2 + cx + d be a polynomial with real coefficients and real roots. If |f(i)|=1where i=sqrt(-1) , then the value of a +b+c+d is

If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f(c)=-1,f(d)=2, f(e)=0 where a < b < c < d e, then the minimum number of zeroes of g(x) = f'(x)^2+f''(x)f(x) in the interval [a, e] is

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

STATEMENT 1: If f(x) is continuous on [a , b] , then there exists a point c in (a , b) such that int_a^bf(x)dx=f(c)(b-a) STATEMENT 2: For a