Q.1.Let a,b,c be real.ax²+bx+c has real roots alpha and beta (alpha>beta).Find the condition on the roots,in relation to p,so that (p²)+(c/a) +(p).mod(b/a)<0.

(alpha, beta =A,B for convenience) p^2 + c/a +p.mod(b/a) < 0 =>p^2 + A*B +p.mod(A+B) < 0 Case1 - A+B > 0 p^2 + A*B +p(A+B) < 0 which is a quadratic in itself, and is 0 at p=-A,-B. => -A < p < -B (from wavy curve) Case2 - A+B < 0 p^2 + A*B - p(A+B) < 0 p^2 + A*B - p(A+B)= 0 for p=A,B => B< p