`f(x) = ax^2 + bx + c `and `g(x) = px^2 + qx + r` if `a^2+b^2+c^2-2a+4b-2c+6=0 a,b,c in R` and `g(0) = 2`, `g'(0)=-3` and `gprimeprime(0)=2` The value of ` f(1)+ g(1)` is

If f(x) =ax^(2) +bx + c, g(x)= -ax^(2) + bx +c " where " ac ne 0 " then " f(x).g(x)=0 has

Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R . Then (a) a+c^2 2b (c) a-3b+c^2 < 0 (d) none of these

Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R . Then (a) a+c^2 2b (c) a-3b+c^2 < 0 (d) none of these

If f(x)=ax^2+bx+c and g(x)=px^2+qx with g(1)=f(1) , g(2)-f(2)=1 and g(3)-f(3)=4 then g(4)-f(4) is

If a, b, c in R and 2a + 3b + 6c = 0, then the equation ax^(2) + bx + c = 0 has

Let a,b,c be the roots of the equation x^(4)+x^(3)+x^(2)+x-1=0. Let f(x)=x^(6)-6x^(2)+6x+7 and g(x)=px^(2)+qx+r , (p,q,r in R,p!=0). If f(a)=g(a); f(b)=g(b) and f(c)=g(c); then the value of (2)/(g(1)) is

Let f(x) = ax^(2)+bx+c , g(x) =px^(2)+qx+r , such that f(1)=g(1),f(2)=g(2) and f(3)-g(3)=2. then f(4)-g(4) is -