InterviewSolution
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InterviewSolution
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If the roots of the equation `x^2-2a x+a^2-a-3=0`are ra and less than 3, then`a |
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Answer» Correct Answer - A Let `f(x) = x^(2) - 2ax + a^(2) + a -3`. Clearly, y = f(x) represents a parabola opening upward. If roots of f(x) = 0 are less than 3, we must have (i) Discriminant `gt 0` (ii) x-coordinate of vertex of y = f(x) is less than 3 (iii) 3 lies outside the roots of `f(x) = 0 i.e. f(3) gt 0` Now, (i) Discriminant `ge 0` `rArr" "4a^(2) -4(a^(2) + a - 3) ge 0 rArr -4 (a-3) ge 0 rArr a - 3 le 0` `rArr" "a le 3" "...(i)` (ii) x-coordinate of vertex `lt 3` `rArr" "a lt 3" "...(ii)` (iii) `f(3) lt 0 rArr a^(2) - 5a + 6 gt 0 rArr (a-2) (a-3) gt 0` `rArr" "a lt 2 or a gt 3" "...(iii)` From (i), (ii) and (iii), we get `a lt 2`. |
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