Polynomials of degree 2

Let f(x) be a polynomial of degree 2 satisfying f(0)=1, f(0) =-2 and f''(0)=6 , then int_(-1)^(2) f(x) is equal to

Evaluate: intf(x)/(x^3-1)dx , where f(x) is a polynomial of degree 2 in x such that f(0)=f(1)=3f(2)=-3

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that "phi(x)=|{:(f(x),g(x),h(x)),(f'(x),g'(x),h'(x)),(f''(x),g''(x),h''(x)):}| is a constant polynomial.

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that phi(x)=|f(x)g(x)h(x)f'(x)g'(x h '(x)f' '(x)g' '(x )h ' '(x)| is:

A polynomial of degree 2 which takes values y_0,y_1,y_2 at points x_0,x_1,x_2 respectively , is given by p(x) = ((x-x_1)(x-x_2))/((x_0-x_1)(x_0-x_2)) y_0 + ((x-x_0)(x-x_2))/((x_1-x_0)(x_1-x_2)) y_1 + ((x-x_0)(x-x_1))/((x_2-x_0)(x_2-x_1)) y_2 A polynomial of degree 2 which takes values y_0, y_0, y_1 at points x_0, x_(0+t), x_1 t!=0 is given by

If int(f(x))/(x^(3)-1)dx , where f(x) is a polynomial of degree 2 in x such that f(0)=f(1)=3f(2)=-3 and int(f(x))/(x^(3)-1)dx=-log|x-1|+log|x^(2)+x+1|+(m)/(sqrt(n))tan^(-1)((2x+1)/(sqrt(3)))+C . Then (2m+n) is

sqrt(2) is a polynomial of degree

The expression [x+(x^(3)-1)^((1)/(2))]^(5)+[x-(x^(3)-1)^((1)/(2))]^(5) is a polynomial of degree