InterviewSolution
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InterviewSolution
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Let `f(x)=ax^(2)+bx+c`, `a ne 0`, `a`, `b`, `c in I`. Suppose that `f(1)=0`, `50 lt f(7) lt 60 ` and `70 lt f(8) lt 80`. Number of integral values of `x` for which `f(x) lt 0` isA. `0`B. `1`C. `2`D. `3` |
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Answer» Correct Answer - B `f(x)=ax^(2)+bx+c`, `a ne 0`, `a,b,c in I` `f(1)=0` ……..`(i)` `implies a+b+c=0` `50 lt f(7) lt 60` `50 lt 49a+7b+c lt 60` `implies 50 lt 48a+6b lt 60` `implies (50)/(6) lt 8a+b lt 10` `implies 8a+b=9`……`(ii)` Also `70 lt f(8) lt 80` `implies 70 lt 64a+8b+c lt 80` `implies70 lt 63a+7b lt 80` `implies 10 lt 9a+b lt (80)/(7)` `implies 9a+b=11`.........`(iii)` From `(i)`, `(ii)` and `(iii)`, `a=2`, `b=-7`, `c=5` `implies f(x)=2x^(2)-7x+5=(2x-5)(x-1)` `=2(x^(2)-(7)/(2)x+(5)/(2))` `=2((x-(7)/(4))^(2)-(9)/(16))` `implies f(x)` has least value `-(9)/(8)` `f(x) lt 0 implies (2x-5)(x-1) lt 0implies1 lt x lt 5//2` |
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