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Let f (x) = ax^(2)+bx+c where a, b, c ar...

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 is

A

2

B

3

C

4

D

5 or more

Text Solution

Verified by Experts

The correct Answer is:
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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