If `ax^(2) + bx + c = 0 ` has imaginary roots and a - b + c ` gt` 0 .
then the set of point (x, y) satisfying the equation
`|a (x^(2) + (y)/(a)) + (b + 1) x + c| = |ax^(2) + bx + c|+ |x + y|`
of the region in the xy- plane which is

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 .