How to write a polynomial function of least degree with integral coefficients that has given zeros

Question

1) -3/4, 1, 0

2) -2/5, 5/3, 0, -1

3) -3, 1/5, 2

4) -5/4, -1/3, 3

Answer 1

I will do the first one for you; you should do the rest.

Note that the second one is a quartic (4th degree) polynomial.

[x + (3/4)(x-1)x

(1/4)(4x + 3)(x-1)x = (1/4)($4x^3-x^2-3x$)