InterviewSolution
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InterviewSolution
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If both the roots of `a x^2+a x+1=0`are less than 1, then find the exhaustive range of values of `adot` |
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Answer» Both roots of `ax^(2) + ax + 1 = 0` are less then 1 . Compare this equation with `Ax^(2) + Bx + C = 0` . Then, the required conditions are (i) ` D = a^(2) - 4a ge 0 rArr a in (-infty, 0 ]cap [4, infty)` (1) (ii) `- (B)/(2A) gt 1 rArr - (a)/(2a)lt 1 ` (which is always true as a `ne`0) (iii) ` Af(1) gt 0 ` `rArr a(2a + 1) gt 0` `rArr ain (-infty,-(1)/(2)) cap (0, infty).` (2) From (1) and (2) , `a in (-infty, - 1//2) cap [4, infty)` . |
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