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The value of 'k' for which one root of t...

The value of 'k' for which one root of the equation `x^2 - (k+1) x + k^2 + k - 8 = 0` exceeds 2 and the other is less than 2, are given by:

Text Solution

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Given equation is,
`x^2-(k+1)x+k^2+k-8 = 0`
It is a quadratic equation that have two different roots.
`:. D > 0`
`=>(k+1)^2 - 4(k^2+k-8) gt 0`
`=>k^2+2k+1-4k^2-4k+32 gt 0`
`=>-3k^2-2k+33 gt 0`
`=> 3k^2+2k-33 lt 0`
...
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