If `a x 62+b x+c=0` has imaginary roots and `a-b+c >0` then the set of points `(x ,y)` satisfying the equation `|a(x^2y/a)+(b+1)x+c|=|a x^2+b x+c|+|x+y|` consists of the region in the `x y-p l a n e` which is on or above the bisector of I and III quadrant on or above the bisector of II and IV quadrant on or below the bisector of I and III quadrant on or below the bisector of II and IV quadrant

Options

A. on or above the bisector of I and III quadrant
B. on or above the bisector of II and IV quadent
C. on or below the bisector of I and III quadrant
D. on or below the bisector of II and IV quadrant .

Answer

2

Explanation

`|a(x^(2) + (y)/(a)) + (b + 1)x + c |= |ax^(2) + bx + c| + |x + y|`
`rArr [ (ax^(2)= bx + c) + (x + y)| = |ax^(2) + bx + c |+ |x + y|` (1)
Now ` f(x) = ax^(2) + bx + c = 0 ` has imaginary roots and
` a - b + c gt 0 or f(-1) gt 0 `
`rArr f(x) = ax^(2) + bx + c gt 0` for all real values of x
`rArr x + y ge 0 `
`rArr (x , y)` lies on or above the bisector of II and Iv quadrants .