" (ix) "x^(3)-x^(2)+ax+x-a-1

If Rolle's theorem holds for the function f(x)=x^(3)-ax^(2)+bx-4, x in [1,2] with f'((4)/(3))=0 , then ordered pair (a, b) is equal to :

The set of values of a for which f(x)=x^(3)-ax^(2)+48x+1 is increasing for all real values of x is

It is given that for the function f given by f(x)=x^(3)+bx^(2)+ax,x in[1,3]. Rolles theorem holds with c=2+(1)/(sqrt(3)). Find the values of a and b

It is given that for the function f given by f(x)=x^(3)+bx^(2)+ax,x in [1,3] . Rolle's theorem holds with c=2+(1)/(sqrt(3)) . Find the values of a and b.

If 4x + 3a = 0 , then what is the value of (x^(2) + ax + a^(2))/(x^(3) - a^(3)) -(x^(2) -ax + a^(2))/(x^(3) + a^(3)) ?

If x=-(1)/(2) is a zero of the polynomial p(x)=8x^(3)-ax^(2)-x+2, find the value of

" The function "f(x)=(a+2)x^(3)-3ax^(2)+9ax-1" is always decreasing "AA x in R" .Then the range of "a" is "

Find the values 'a' for which the function f(x)=(a+2)x^(3)-3ax^(2)+9ax-1 decreases for all real values of x

Find the value of a so that (x+1) may be a factor of 2x^(3)-ax^(2)-(2a-3x+2)

Factorize the following expressions x^3-x^2+ax+x-a-1