Integer Coefficients

Algebra Level 3

Find the smallest positive integer \(e \) such that the polynomial \( ax^4 + bx^3 + cx^2 +dx + e \) has integer coefficients and has roots at \( -2\), \(3\), \( 5/3 \), and \(-1/2\).

Details and assumptions

A root of a polynomial is a number \(r\) where the polynomial is equal to 0. For example, the number \(r = 3 \) is a root of the polynomial \( 2x - 6\).

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