Let `P(x)=x^3+ax^2+bx+c` be a polynomial with real coefficients, `c!=0andx_1,x_2,x_3` be the roots of `P(x)`. Determine the polynomial `Q(x)` whose roots are `1/x_1,1/x_2,1/x_3` .

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

Let f(x) = x^4 + ax^3 + bx^2 + cx + d be a polynomial with real coefficients and real roots. If |f(i)|=1where i=sqrt(-1), then the value of a +b+c+d is

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)=x^(3)+ax^(2)+bx+c be a cubic polynomial with real coefficients and all real roots.Also |f(iota|=1 where iota=sqrt(-1) statement-1: All 3roots of f(x)=0 are zero Statement-2: a+b+c=0

Let P(x) be a cubic polynomial such that coefficient of x^(3) is 1;p(1)=1,p(2)=2,p(3)=3 then the value of p(4) is :

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

Let P(x)=x^(2)+bx+c be a quadratic polynomial with real coefficients such that int_(0)^(1)P(x)dx=1 and P(x) leaves remainder 5 when it is divided by (x - 2). Then the value of 9(b + c) is equal to:

Let g(x) and h(x) be two polynomials with real coefficients. If p(x) = g(x^(3)) + xh(x^(3)) is divisible by x^(2) + x + 1 , then

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