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If the inequality (m x^2+3x+4+2x)//(x^2+...

If the inequality `(m x^2+3x+4+2x)//(x^2+2x+2)<5` is satisfied for all `x in R ,` then find the value of `mdot`

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We have ,
`x^(2) 2x + 2 = (x-1)^(2) + 1 gt 0, AA x in` R
Therefore, `(mx^(2) + 3x + 4)/(x^(2) + 2x + 2) lt 5`
or `(m - 5) x^(2) - 7x - 6 lt 0, AA x in` R
`rArr m - 5lt 0 and D lt` 0
`rArr m lt 5 and 49 + 24 (m - 5) - lt`0
`rArr m lt (71)/(24)`
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