If ax2 + bx + c = 0 has imaginary roots and a - b + c > 0, then the set of points (x, y) satisfying the equation ax2+ya+(b+1)x+c=ax2+bx+c+|x+y| consists of the region in the xy-plane which is

ax2+ya+(b+1)x+c=ax2+bx+c+|x+y|⇒ ax2+bx+c+(x+y)=ax2+bx+c+|x+y|            (1)Now f(x)=ax2+bx+c=0 has imaginary roots and a−b+c>0 or f(−1)>0⇒ f(x)=ax2+bx+c>0 for all real values of x⇒ x+y≥0⇒ (x,y) lies on or above the bisector of II and IV quadrants