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If zeros of x^3 - 3p x^2 + qx - r are in...

If zeros of `x^3 - 3p x^2 + qx - r` are in A.P., then

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As roots are in A.P. so, they can be,
`a-d,a,a+d`.
Now, sum of roots, `-(-3p)/1 = a-d+a+a+d`
`=> 3a = 3p=> a = p->(1)`
Product of roots,
`a(a-d)(a+d) = r/1`
`=>a(a^2-d^2) = r`
`=>(a^2-d^2) = r/a`
...
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