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If `a, b` and `c` are positive real and `a = 2b + 3c`, then the equation `ax^(2) + bx + c = 0` has real roots forA. `|(b)/(c) - 4|ge 2sqrt(7)`B. `|(c)/(b) - 4|ge 2sqrt(7)`C. `|(a)/(c) - 11|ge 4sqrt(7)`D. `|(a)/(b) + 11|ge 1sqrt((13)/(3))` |
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Answer» Correct Answer - A::C `a = 2b + 3c` Equation `ax^(2) + bx + c = 0` has real roots `b^(2) - 4ac ge 0 rArr b^(2) - 4(2b + 3c)c ge 0` `rArr c^(2)[((b)/(c))^(2) - 8((b)/(c))-12]ge0` `rArr ((b)/(c))^(2) - 8((b)/(c)) + 16 ge 28` `rArr ((b)/(c) - 4)^(2) ge 28 rArr |(b)/(c)-4|ge2sqrt(7)` Similarly `|(a)/(c)-11|ge4sqrt(7)` |
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