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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 isA. on or above the bisector of I and III quadrantB. on or above the bisector of II and IV quadentC. on or below the bisector of I and III quadrantD. on or below the bisector of II and IV quadrant . |
Answer» Correct Answer - 2 `|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 . |
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