Find the condition that the zeroes of the polynomial `f(x) = x^3 – px^2 + qx - r` may be in arithmetic progression.

Explanation

Given`P(x)=x^3−px^2+qx−r`

Let thee roots be `(a-d),a,(a+d)`

sum of roots, `3a=P=>a=P/3`

Product,` (a^2−d^2)a=r=>(P^2/9​−d^2)=(3r)/P`
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=`d^2=P^2/9​−(3r)/P`

thus,

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`(a+d)(a−d)+a(a+d)+a(a−d)`

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