InterviewSolution
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InterviewSolution
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Answer» Correct Answer - `a to r; b to r; c to q; d to p ` `ator,btor,ctoq,d""to""p` `(m-2)x^(2)-(8-2m)x-(8-3m)=0` has roots of opposite signs. The product of roots is `-(8-3m)/(m-2)lt0` or `(3m-8)/(m-2)lt0` or `2ltmlt8//3` (b) Exactly one root of equation `x^(2)-m(2x-8)-15=0` lies in interval (0,1). `f(0)f(1)lt0` `implies(0-m(-8)-14)(1-m(-6)-15)lt0` `implies(8m-15)(6m-14)lt0` `implies15//8ltmlt7//3` (c) `x^(2)+2(m+1)x+9m-5=0` has both roots negative. Hence, sum of roots is `-2(m+1)ltormgt-1" "(1)` Product of roots is `9m-5gt0impliesmgt5//9" "(2)` Discriminant, `Dge0implies4(m+1)^(2)-4(9m-5)ge0` `impliesm^(2)-7m+6ge0` `impliesmle1ormge0" "(3)` Hence, for (1), (2),and (3), we get `m""in((5)/(9),1]uu[6,oo)` (d) `f(x)=x^(2)+2(m-1)x+m+5=0` has one root less than 1 and the other root greater than 1. Hence, `f(1)lt0` `implies1+2(m-1)+m+5lt0` `impliesmlt-4//3` |
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