Let `P(x)` be a polynomial with real coefficients, Let `a , b in R ,a

Define a polynomial with real coefficients.

Question Number 2 Let P(x) be a polynomial with real coefficients such that P(sin2 ) P(cos2 x). for all re [0, ?/2]. Consider the following statements: I. P(x) is an even function II. P(x) can be expressed as a polynomial in (2x - 1)2. III. P(x) is a polynomial of even degree Then Bonly I and II are tue D. all are true A. all are false C only II and III are true

Question Number 2 Let P(x) be a polynomial with real coefficients such that P(sin2 ) P(cos2 x). for all re [0, ?/2]. Consider the following statements: I. P(x) is an even function II. P(x) can be expressed as a polynomial in (2x - 1)2. III. P(x) is a polynomial of even degree Then Bonly I and II are tue D. all are true A. all are false C only II and III are true

Let f(x) be a polynomial with real coefficients such that f(0)=1 and for all x ,f(x)f(2x^(2))=f(2x^(3)+x) The number of real roots of f(x) is:

Let f(x) is a cubic polynomial with real coefficients, x in R such that f''(3)=0 , f'(5)=0 . If f(3)=1 and f(5)=-3 , then f(1) is equal to-

Let P(x) be a polynomial of degree n with real coefficients and is non negative for all real x then P(x) + P^(1)(x)+ ...+P^(n)(x) is

Let P(x) be quadratic polynomical with real coefficient such tht for all real x the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then Sum of all coefficients of P(x) can not be

Let p (x) be a polynomial with real coefficient and p (x)=p'(x) =x^(2)+2x+1. Find P (1).

Let P(x) be a quadratic polynomial with real coefficients such that for all real x the relation 2(1+P(x))=P(x-1)+P(x+1) holds. If P(0)=8 and P(2)=32, then Sum of all the coefficients of P(x) is: