Graph of Quadratic funtion `f(x)=ax^2+bx+c` for different cases (i) If `agt0 and Dlt0` (ii) `alt0 and Dlt0` (iii)`agt0 and D=0` (iv) `agt0 and Dgt0` (v) `alt0 and D=0` (vi) `alt0 and Dgt0`

If ax+by+c=0 is a normal to hyperbola xy=1 , then (A) alt0, blt0 (B) alt0, bgt0 (C) agt0, bgt0 (D) agt0, blt0

For a quadratic equation, alt0 and b^2=4ac , determine the nature of the graph.

[ 9.Let f(x)=ax+sin2x+b ,then f(x)=0 has (A) exactly one positive real root,if agt2 and blt0 (B) exactly one positive real root,if agt2 and bgt0 (C) Both(A)&(B) (D) None of these ]

If agt0 and blt0, then sqrt(a)sqrt(b) is equal to (where, i=sqrt(-1))

If x and a area real numbers such that agt0 and |x|gta then:

Let alpha and beta be the real and distinct roots of the equation ax^2+bx+c=|c|,(agt0) and p,q be the real and distinct roots of the equation ax^2+bx+c=0. Then which of the following is true? (A) p and q lie between alpha and beta (B) p and q lies outside (alpha, beta) (C) only p lies between alpha and beta (D) only q lies between (alpha and beta)