Find the condition that the zeros of the polynomial may be in A.P.

Let are the zeros of the given polynomial.

Sum of the zeros =

=

=

=

Since is the zero of the polynomial, therefore

⇒ f(a) = a3 + 3pa2 + 3qa + r = 0

⇒ a3 + 3pa2 + 3qa + r = 0

=, we get

⇒ -p3 + 3p3 - 3pq + r = 0
⇒ 2p3 - 3pq + r = 0

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