Determine all polynomial p(x) with rational coefficient so that for all x with `|x|le1`,
`p(x)=p((-x+sqrt(3-3x^(2)))/(2))`.

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 quadratic polynomical with real coefficient such tht for all real x(1) the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then If the range of P(x) is [m, oo) then 'm' is less then

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

Let P(x) =x^(2)+ 1/2x + b and Q(x) = x^(2) + cx + d be two polynomials with real coefficients such that P(x) Q(x) = Q(P(x)) for all real x. Find all the real roots of P(Q(x)) =0.

For a polynomial p (x) , the value of p(3) is −2 . Which of the following must be true about p (x) ?

Let p(x) be a polynomial of degree 6 with leading coefficient unity and p(-x)=p(x)AAxepsilonR . Also (p(1)+3)^(2)+p^(2)(2)+(p(3)-5)^(2)=0 then sqrt(-4-p(0)) is….

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : p(x)=x^3-3x^2+5x-3,g(x)=x^2-2

Let P(x) be a polynomial with real coefficients such that P(sin^2x) = P(cos^2x) , for all xϵ[0,π/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

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : p(x)=x^4-3x^2+4x+5,g(x)=x^2+1-x

Let p(x)=0 be a polynomial equation of the least possible degree, with rational coefficients having ""^(3)sqrt7 +""^(3)sqrt49 as one of its roots. Then product of all the roots of p(x)=0 is a. 56 b. 63 c. 7 d. 49