If `f(x)=x^3+x^2-a x+b` is divisible by `x^2-x` write the values of `a` and `b` .

If f(x)=x^3=x^2+a x+b is divisible by x^2-x , then find the value of f(2)dot

If f(x)=x^3-x^2+a x+b is divisible by x^2-x , then find the value of f(2)dot

If x^3+a x^2-b x+10 is divisible by x^2-3x+2, find the values of a and b .

If x^3+a x^2-b x+10 is divisible by x^2-3x+2, find the values of a and b .

If f(x) = 2x^4 - 13 x^2 + ax +b is divisible by x^2 -3x +2 then (a,b)=

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

If f(x)=x^3-3x^2+2x+a is divisible by x-1, then find the remainder when f(x) is divided by x-2.

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)) .

Let P(x) and Q(x) be two polynomials.Suppose that f(x) = P(x^3) + x Q(x^3) is divisible by x^2 + x+1, then (a) P(x) is divisible by (x-1),but Q(x) is not divisible by x -1 (b) Q(x) is divisible by (x-1), but P(x) is not divisible by x-1 (c) Both P(x) and Q(x) are divisible by x-1 (d) f(x) is divisible by x-1

The graph of the polynomial f(x)=a x^2+b x+c is as shown in Fig. 2.20. Write the value of b^2-4a c and the number of real zeros of f(x) . (FIGURE)