Let `P(x)=a_0+a_1x^2+a_2x^4++a_n x^(2n)` be a polynomial in a real variable `x` with `0

If P(x) = a _0 + a _1 x ^(2) + a _2 x^(4) + … + a _n x ^(2n) is a polynomial in a real variable x with 0 lt a _0 lt a _1 lt a _2 lt … lt a_n . Then, the function P (x) has

If p(x)=a_(0)+a_(1)x^(2)+a_(2)x^(4)+...+a_(n)x^(2n) is a polynomial in a real variable x with 0< a_(0)< a_(1)< a_(2)<...< a_(3) . Then,the function p(x) has

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

Let P(x) =a_(0)+a_(1)x^2+a_(2)x^(4)+cdots+a_(n)x^(2n) with all a_(i) gt0 , i=0,1,2,3, cdots ,n . Then P(x) has