" 21.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 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

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.Then: 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 .

Let p(x) be a quadratic polynomial with real coefficient satisfying x^(2)-2x+2<=p(x)<=2x^(2)-4x+3AA x in R and suppose p(11)=181. Find p(6)

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.

Let P(x)=x^(2)+(1)/(2)x+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

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 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)=x^(10)+a_(2)x^(8)+a_(3)x^(6)+a_(4)x^(4)+a_(5)x^(2) be a polynomial with real coefficients.If P(1) and P(2)=5, then the minimum- number of distinct real zeroes of P(x) is