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What is the value of m which satisfies...

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`

Text Solution

Verified by Experts

The correct Answer is:
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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