Let ` f(x)= a_0x^n +a_1x^(n-1) +a_2x^(n-2) +.......+a_n,(a_0 !=0) ` if ` a_0+a_1 +a+_2+...... +a_n =0 ` then the root of `f(x) ` is

let f(x)=a_0+a_1x^2+a_2x^4+............a_nx^(2n) where 0< a_0 < a_1 < a_3 ............< a_n then f(x) has

If (1+x)^n = a_0+a_1x+a_2x^2+......+a_nx^n , find the sum a_0+a_4 + a_8 + a_12 + ….. .

If (1 - x + x^2)^n = a_0 + a_1x + a_2x^2 +...+ a_(2n) x^(2n) then a_0 + a_2 + a_4 +...+ a_(2n) is equal to

If (1 - x + x^2)^n = a_0 + a_1 x + a_2x^2 + ..... + a_(2n)x^(2n) then a_0 + a_2 + a_4 + ... + a_(2n) equals

Let a_0x^n + a_1 x^(n-1) + ... + a_(n-1) x + a_n = 0 be the nth degree equation with a_0, a_1, ... a_n integers. If p/q is arational root of this equation, then p is a divisor of an and q is a divisor of a_n . If a_0 = 1 , then every rationalroot of this equation must be an integer.

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 < a_0 < a_1 < a_2 <......< a_n . The function P(x) has a. neither a maximum nor a minimum b. only one maximum c. only one minimum d. only one maximum and only one minimum e. none of these

Let (1+x^2)^2 (1+x)^n= A_0 +A_1 x+A_2 x^2 + ...... If A_0, A_1, A_2,........ are in A.P. then the value of n is

Given that (1+x+x^2)^n=a_0+a_1x+a_2x^2+.....+a_(2n)x^(2n) find i) a_0 + a_1 +a_2 .. . . .+ a_(2n) ii) a_0 - a_1 + a_2 - a_3 . . . . + a_(2n) iii) (a_0)^2 - (a_1)^2 . . . . .+ (a_(2n))^2