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Let f `(x) = ax^(2)+bx+c` where a, b, c are integers. Suppose f (1)=0,`40 lt f (6) lt 50, 60 lt f (7) lt 70, and 1000t lt f(50) lt 1000(t+1)` for some integer t. Then the value fo t isA. 2B. 3C. 4D. 5 or more |
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Answer» Correct Answer - C f(x)=`ax^(2)+bx+c` given f (1) = 0 `rArr a+b+c = 0` and `40 lt f(6) lt 50` `rArr 40 lt 36a+6b+c lt 50` `rArr 40 lt 35a+5b lt 50` `rArr 8 lt 7a+b lt 10` 7a+b = integer = 9 …..(1) and `60 lt f(7) lt 70` `rArr 60 lt 49a+7b +c lt 70` `rArr 60 lt 48a+6b lt 70` `rArr 10 lt 8a+b lt 11.6` 8a+b = integer = 11 ....(2) Solving (1)&(2) a =2, b = -5, c = 3 `:. f (x) 2x^(2)-5x+3` f(50) = 4753 `1000 t lt f(50) lt 1000 (t+1)` `(1000 xx 4) lt 4753 lt 1000 (4+1)` `:. t = 4` |
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