`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

f(x)=ax^(2)+bx+c and g(x)=px^(2)+qx+ra^(2)+b^(2)+c^(2)-2a+4b-2c+6=0a,b,c in R and g(0)=2,g'(0)=-3 and g''(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 ne 0 and f(x) ne 0 for all x in R . Then

Consider f g and h are real-valued functions defined on R. Let f(x)-f(-x)=0 for all x in R, g(x) + g(-x)=0 for all x in R and h (x) + h(-x)=0 for all x in R. Also, f(1) = 0,f(4) = 2, f(3) = 6, g(1)=1, g(2)=4, g(3)=5, and h(1)=2, h(3)=5, h(6) = 3 The value of f(g(h(1)))+g(h(f(-3)))+h(f(g(-1))) is equal to

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)=ax^(2)+qx+r , where a , b , c , q , r in R and a lt 0 . If alpha , beta are the roots of f(x)=0 and alpha+delta , beta+delta are the roots of g(x)=0 , then