Let `P(x) = x^10+ a_2x^8 + a_3 x^6+ a_4 x^4 + a_5x^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

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

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 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 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 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^(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

A cubic polynomial p(x) is such that p(1)=1,p(2)=2,p(3)=3 and p(4)=5 then the value of p(6) is