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What is the value of m which satisfies ` 3m^(2) - 21 m + 30 lt 0`?A. `m lt 2 or m gt 5`B. ` m gt 2`C. ` 2 lt m lt 5`D. ` m lt 5`

Answer» Correct Answer - C
`3m^(2) - 21m + 30 lt 0`
or `m^(2) - 7m + 10 lt 0`
or ` m^(2) -5m - 2m + 10 lt 0" "` (factorize)
or ` m(m-5)-2(m-5) lt 0`
or ` (m-2)(m-5) lt 0`
Case I: ` m -2 gt 0 and m - 5 lt 0`
` rArr m gt 2 and m lt 5 rArr 2 lt m lt 5`
Case II: ` m - 2 lt 0 and m - 5 gt 0 rArr m lt 2 and m gt 5`
nothing common
Hence, ` 2 lt m lt 5`


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