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The set of values of p for which the roo...

The set of values of p for which the roots of the equation `3x^2 +2x + p(p-1) =0` are of opposite signs is:

Text Solution

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Let one root is `alpha`. So, second root will be `-alpha`.
`:.` Sum of roots `= alpha-alpha = 0`
`:.` Product of roots `= -alpha^2`
It means product of rootsis less than `0`.
Product of roots in the given equation is `(p(p-1))/3`.
`:. (p(p-1))/3 lt 0`
`=> (p(p-1)) lt 0`
`:.p in ]0,1[`
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