Show that the general quartic (fourth degree) polynomial f(x) x 4 ax 3 bx 2 cx d has either zero or two inflection points, and that the latter case occurs provided that b 3a 2 8

Question: Show that the general quartic (fourth-degree) polynomial f(x) = x 4 + ax 3 + bx 2 + cx + d has either zero or

Show that the general quartic (fourth-degree) polynomial f(x) = x⁴ + ax³ + bx² + cx + d has either zero or two inflection points, and that the latter case occurs provided that b < 3a²/8.

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