InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `a x^2+(b-c)x+a-b-c=0`has unequal real roots for all `c in R ,t h e n``b |
|
Answer» Correct Answer - 3,4 We have, ` D = (b - c)^(2) - 4a(a - b - c) gt 0 ` or ` b^(2) + c^(2) - 2bc - 4a^(2) + 4ab + 4ac gt 0 ` ` or c^(2) + (4a - 2b) c - 4a^(2) + 4ab + b^(2) gt 0 ` for all ` c in ` R Discriminant of the above expression in c must be negative Hence, ` 1(4a = 2b)^(2) - 4 (-4a^(2) + 4ab + b^(2)) lt 0 ` or ` 4a^(2) - 4ab + b ^(2) + 4a^(2) - 4ab - b^(2) lt 0 ` or ` a (a - b) lt 0 ` `rArr a lt 0 and a - b gt 0 or a gt 0 and a - b lt 0 ` `rArr b lt a lt 0 or b gt a gt 0 ` . |
|