If `ax^(9)+bx^(3)+1` is divisible by `x^(2)-x-1` then value of `a` is

If the polynomial 7x^(3)+ax+b is divisible by x^(2)-x+1 , find the value of 2a+b.

If ax^3+ bx - c is divisible by x^2+bx+c , then 'a' is a root of the equation

Let f(x) be a polynomial of degree 6 divisible by x^(3) and having a point of extremum at x = 2 . If f'(x) is divisible by 1 + x^(2) , then find the value of (3f(2))/(f(1)) .

The number of polynomials of the form x^(3)+ax^(2)+bx+c that are divisible by x^(2)+1 , where a, b,cin{1,2,3,4,5,6,7,8,9,10} , is

If x+1 is a factor of ax^(3)+x^(2)-2x+4a-9 , then value of a .

If f(x)=ax^(2)+bx+c and f(x+1)=f(x)+x+1 , then the value of (a+b) is __

The expansion by the binomial theorem of (2 x + (1)/(8) )^(10) is 1024x^(10) + 640x^(9) + ax^(8) + bx^(7) + ... Calculate (i) the numerical value of a and b

let f(x)={(ax+1, if x le 1),(3, if x=1),(bx^2+1,if x > 1)) if f(x) is continuous at x=1 then value of a-b is (A) 0 (B) 1 (C) 2 (D) 4

When f(x)=x^(3)+ax^(2)-bx-8 is divided by x-2, the remainder is zero and when divided by x+1, the remainder is -30. Find the values of 'a' and 'b'.