A quartic polynomial is given to have two distinct inflection points, call those points I₁ and I₂. A line is drawn through these inflection points and intersects the quartic at two other points, call those points P₁ and P₂.

The four points will lay along the line in the order P₁, I₁, I₂, P₂.
Show that segments P₁I₁ and P₂I₂ are congruent.
Find the ratio of segment P₁I₁ to I₁I₂.