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

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

Consider the polynomial f(x)=a x^2+b x+c dot If f(0)=0,f(2)=2, then the minimum value of int_0^2|f^(prime)(x)|dxi s___

A nonzero polynomial with real coefficients has the property that f(x)=f'(x)cdotf''(x). If a is the leading coefficient of f(x), then the value of 1//a is -

If 0 and 1 are the zeroes of the polynomial f (x) = 2x ^(3) - 3x ^(2) + ax +b, then find the values of a and b.

If x be a factor of the polynomial f(x) = (x - a) (x + b) (x - c), then f(0) =

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

A nonzero polynomial with real coefficient has the property that f(x)=f^(prime)(x)dot f^(primeprime)(x)dot If a is the leading coefficient of f(x), then the value of 1/(2a) is____

The function f(x)=a x^3+b x^2+c x+d has three positive roots. If the sum of the roots of f(x) is 4, the larget possible inegal values of c//a is ____________.

f(x) is cubic polynomial with f(x)=18 and f(1)=-1 . Also f(x) has local maxima at x=-1 and f^(prime)(x) has local minima at x=0 , then (A) the distance between (-1,2)a n d(af(a)), where x=a is the point of local minima is 2sqrt(5) (B) f(x) is increasing for x in [1,2sqrt(5]) (C) f(x) has local minima at x=1 (D)the value of f(0)=15

A function is defined as f(x)=x^2-3xdot Find the value of f(2)dot Find the value of x for which f(x)=4.