InterviewSolution
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InterviewSolution
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Let three quadratic equations ` ax^(2) - 2bx + c = 0, bx^(2) - 2 cx + a = 0` and `cx^(2) - ax + b = 0 `, all have only positive roots. Then ltbr. Which of these are always ture?A. `b^(2) = ac `B. `c^(2) = ab `C. each pair of equations has exactly one root commonD. each pair of equations has two roots common |
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Answer» Correct Answer - 1,2,4 For each equation , required condition (i) Dicriminant ` ge 0 rArr b^(2) le ac, c^(2) ge ab , a^(2) ge bc ` (ii) ` f(0) gt 0 rArr c,a,b ge 0 ` (iii) Abscissa of vertex ` gt 0 rArr (b)/(a) gt 0 , (c)/(b) gt 0, (a)/(c) gt0 ` . Now, `b^(2) ac , c^(2) ge ab rArr b^(2) c^(2) ge a^(2) bc rArr bc ge a^(2).` But ` a^(2) ge bc. So, a^(2) = bc ` Similarly, ` b^(2) = ac and c^(2) = ab ` Therefore , a = b= c . |
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