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_2x^8 + a_3 x^6+ a_4 x^4 + a_5x^2 be a polynomial with real coefficients. If P(1)=1 and P(2)=-5 , then the minimum-number of distinct real zeroes of P(x) is

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

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) 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^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+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___________.