Let `P(x)=P(0)+P(1)x+P(2)x^(2)` be a polynomial such that `P(-1)=1` ,then `P(3)` is :

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____________.

Let f(x)= x^(3) + x + 1 and P(x) be a cubic polynomial such that P(0) = -1 and roots of f(0) = 1 ; P(x) = 0 are the squares of the roots of f(x) = 0 . Then find the value of P(4).

If P(x) is a polynomial such that P(x^(2)+1)={P(x)}^(2)+1 and P(0)=0, then P'(0) is equal to

Let f(x)=x^(3)+x+1 , let p(x) be a cubic polynomial such that the roots of p(x)=0 are the squares of the roots of f(x)=0 , then

P(x) is said to be a monic polynomial if its leading coefficient is 1. If P(x) is divided b (x-a) the remainder is given by P(a). If P(a) = 0 then (x-a) is called factor of P(x). If P(x) is a monic polynomial of degree 4 such that P(1) = P(2) = P(3) = P(4) = 2. The value of P(0) is

P(x) is said to be a monic polynomial if its leading coefficient is 1. If P(x) is divided b (x-a) the remainder is given by P(a). If P(a) = 0 then (x-a) is called factor of P(x). If P(x) is a monic polynomial of degree 4 such that P(1) = P(2) = P(3) = P(4) = 2. The value of P(5) is

Let P(x) and Q(x) be two polynomials.Suppose that f(x) = P(x^3) + x Q(x^3) is divisible by x^2 + x+1, then (a) P(x) is divisible by (x-1),but Q(x) is not divisible by x -1 (b) Q(x) is divisible by (x-1), but P(x) is not divisible by x-1 (c) Both P(x) and Q(x) are divisible by x-1 (d) f(x) is divisible by x-1

Let P_n(x) =1+2x+3x^2+............+(n+1)x^n be a polynomial such that n is even.The number of real roots of P_n(x)=0 is

If p(x) is a polynomial function and p(-1)=3, which statement is true?

Let P_n(ix) =1+2x+3x^2+............+(n+1)x^n be a polynomial such that n is even.The number of real roots of P_n(x)=0 is