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If one zero of the cubic polynomial px^3...

If one zero of the cubic polynomial `px^3+qx^2+rx+s` is 2, then the square of the difference of other two zeroes is:

Text Solution

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`alpha+beta+2=-q/p`
`alphabeta+2beta+2alpha=r/p`
`2alphabeta=-s/p`
`(alpha-beta)^2=alpha^2+beta^2-2alphabeta`
`(alpha-beta)^2=(alpha+beta)^2-4alphabeta`
`alpha+beta=-q/p-2`
`(alpha-beta)^2=(alpha+beta)^2-4alphabeta`
`=(-q/p-2)^2-4(-s/2p)`
...
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