Let `P(x0=x^3-8x^2+c x-d` be a polynomial with real coefficients and with all it roots being distinct positive integers. Then number of possible value of `c` is___________.

Let P(x)=x^(3)-8x^(2)+cx-d be a polynomial with real coefficients and with all it roots being distinct positive integers.Then number of possible value of c is

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 P(x) be a non-zero polynomial with integer coefficients.If P(n) is divisible for each positive integer n, what is the vale of P(0)?

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 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 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:

If f(x) is a polynomial of degree 5 with real coefficients such that f(|x|)=0 has 8 real roots, then f(x)=0 has