Let for `a!=a_(1)!=0f(x)=ax^(2)+bx+c, g(x)=a_(1)x^(2)+b_(1)x+c_(1)` and `p(x)=f(x)-g(x)`. If `p(x)=0` only for `x=(-1)` and `p(-2)=2`, the value of `p(2)` is

Let for a != a_1 != 0 , f(x)=ax^2+bx+c , g(x)=a_1x^2+b_1x+c_1 and p(x) = f(x) - g(x) . If p(x) = 0 only for x = -1 and p(-2) = 2 then the value of p(2) .

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

If f(x)=x^2+x-42 and f(p-1)=0. what is a positive value of p ?

f(x) = (5-x^(p))^((1)/(2)) . If the value of f(f(2)) = 2 , what is the value of p ?

If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of the form of ax^(2)+bx+c , then the value of f(1) is

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Divide p(x) by g(x) , where p(x) = p(x)=x+3x^2-1 and g(x)=1+x

Let f(x)=2x+1 and g(x)=int(f(x))/(x^(2)(x+1)^(2))dx . If 6g(2)+1=0 then g(-(1)/(2)) is equal to

Let (1 + x^(2))^(2) (1 + x)^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … if a_(1),a_(2) " and " a_(3) are in A.P , the value of n is

Let g(x)=2f(x/2)+f(1-x) and f^(primeprime)(x)<0 in 0<=x<=1 then g(x)