Question

Find the condition which must be satisfied by the coefficients of the polynomial f(x) = x 3 – px 2 + q x –r when the sum of its two zeroes is zero.

Answer 1

Answer:

In the cubic , let roots be a ,-a ,b :

as sum of two roots is zero.

So -(-p) = sum of roots taken one at a time. So p = a-a+b = b.

So q = sum of roots taken two at a time. So q = ab - ab - aa = -(a^2)

So -(-r) = product of roots

So r = -aab = -b.(a^2) = p.q

So the condition is : r = p.q

Then sum of at least two roots is Zero.

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