Let `P(x)=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) 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

x^3 + x^2 + 16 is exactly divisible by x, where x is a positive integer. The number of all such possible values of x is

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:

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)=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