If `P(x)=x^3-x^2+x+1`,then the value of `(P(-1)+P(1))/2` is

If P(x)=x^(3)-1 then the value of P(1)+P(-1) is

Let a,b,c, d be the roots of x ^(4) -x ^(3)-x ^(2) -1=0. Also consider P (x) =x ^(6)-x ^(5) -x ^(3) -x ^(2) -x, then the value of p (a) +p(b) +p(c ) +p(d) is equal to :

If p(x) =x^(2)-4x+3, then evaluate p(2) -p(-1)+p((1)/(2)) .

Consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1, and ("lim")_(xvec0)((p(x))/(x^3)-2)=4 . Then the value of [P(1)] is (where [.] represents greatest integer function)___

If (x+1) and (x-1) are factors of p(x)=ax^3+x^2-2x+b find the values of a & b .

P(x) be a polynomial of degree 3 satisfying P(-1) =10 , P(1) =-6 and p(x) has maxima at x = -1 and p(x) has minima at x=1 then The value of P(1) is

If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6,p!=1 , then the value of p/x is a. 1/3 b. 3 c. 1/2 d. 2

If 1 is a zero of the polynomial p(x)=a x^2-3(a-1)x-1 , then find the value of a .

Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1,P(2)=8,P(3)=27 ,P(4)=64 then the value of 152-P(5) is____________.

P=x^3-1/x^3, Q=x-1/x x in (1,oo) then minimum value of P/(sqrt(3)Q^2)