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Dear Sajin,
Divide ax^3+bx+c by x^2+px+1. You will get remainder as
By Factor theorem, remainder must be zero in this case.
Thus, coefficient of x = 0 and constant term = 0.
Hence, b - a + ap^2 = 0 and c + ap = 0
From second eqn. we get p = -c/a. Now, putting this value in the first one, we get:
b - a + c^2/a = 0.
Multiplying both sides by a, we get ab - a^2 + c^2 = 0,
OR, a^2 - c^2 = ab
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