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

The number of distinct real roots of x^4-4x^3+12 x ^2+x-1=0 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 f(x) be a polynomial of degree 5 such that f(|x|)=0 has 8 real distinct , Then number of real roots of f(x)=0 is ________.

The number of distinct real roots of the equation sin pi x=x^(2)-x+(5)/(4) is

Column I: Equation, Column II: No. of roots x^2tanx=1,x in [0,2pi] , p. 5 2^(cosx)=|sinx|,x in [0,2pi] , q. 2 If f(x) is a polynomial of degree 5 with real coefficients such that f(|x|)=0 has 8 real roots, then the number of roots of f(x)=0. , r. 3 7^(|x|)(|5-|x||)=1 , s. 4

Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1, P(2)=8, P(3)=27, P(4)=64 then find P(10)

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

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

Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1,P(2)=8,+P(3)=27 ,P(4)=64 then the value of 152-P(5) is____________.