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The number of integral values of m for w...

The number of integral values of m for which the quadratic expression `(1 + 2m)x^(2) - 2(1 + 3m)x + 4(1 + m), x in R`, is always positive is

A

8

B

3

C

7

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
`(1+2m)x^(2) - 2(1+3m) + 4(1+m) gt 0 AA x in R rArr 1 + 2m gt 0` & `D lt 0`
`m gt -(1)/(2)` & `4(1+3m)^(2) - 16(1+2m)(1+m) lt 0 , (1+3m)^(2) -4(2m+1)(1+m) lt 0`
`m^(2) - 6m - 3 lt 0 , 3-2sqrt(3) lt m lt 3 + 2sqrt(3) rArr 0 le m le 6`
Hence 7 integral values of m.
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