if `f(x)=1+2x^2+4x^4+6x^6.....100x^100` is a polynomial in real variable x, then `f(x)` has

If f(x)=1+x+x^(2)+.......+x^(100) then f'(1)=-

Let f(x) is a cubic polynomial which is having local maximum at (1, 2) and f'(x) has local extremum at x = 0. If f(0) = 1 then answer the following Number of real roots of the equation f(x) - f(-x) = 6x - 10 is

If the polynomial f(x)=x^4-6x^3+16 x^2-25 x+10 is divided by another polynomial x^2-2x+k , the remainder comes out to be x+a , find k and a .

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

If the polynomial f(x)=x^(4)-6x^(3)+16x^(2)-25x+10 is divided by another polynomial x^(2)-2x+k the remainder comes out to be x+a, find k and a.

If f(x) = 1+x + x^(2)/2 + …. + x^(100)/100 , then f^(')(1) is equal to

Let f(x)=2^100x+1,g(x)=3^100x+1 Then the set of real numbers x such that f(g(x))=x is

Consider the polynomial f(x)=1 + 2x + 3x^2 +4x^3 for all x in R So f(x) has exactly one real root in the interval

Let f(x) be a non-constant polynomial with real coefficients such that f((1)/(2))=100 and f(x) le 100 for all real x. Which of the following statements is NOT necessarily true ?