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Cubic Polynomial

Find the cond...

Question

Find the condition that the zeros of the polynomial $f (x) = x^{3} + 3 p x^{2} + 3 q x + r$ may be in A.P.

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Q. Find the condition that the zeros of the polynomial f(x) = x³ + 3px² + 3qx + r may be in A.P.

Q. If zeros of the polynomial f(x) = x³ − 3px² + qx − r are in A.P., then

(a) 2p³ = pq − r
(b) 2p³ = pq + r
(c) p³ = pq − r
(d) None of these

Q. Find the condition that the zeros of the polynomial f(x) = x³ + 3px² + 3qx + r may be in A.P.

Q. If zeros of the polynomial

f (x) = x^{3} - 3 p x^{2} + q x - r

are in A.P., then

Q. If the roots of the equation

x^{3} + 3 p x^{2} + 3 q x + r = 0

are in A.P, then the condition is:

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