How do you write a polynomial function of the least degree with integral coefficients of given zeros?

Question

anonymous · Answer

subtract x from each given zero, and multiply the terms together

anonymous · Answer

spose we are given the set of roots:  (r1, r2, r3, r4, ..., rk)

subtract x from each root:

(r1-x, r2-x, r3-x, r4-x, ..., rk-x)

now multiply all the terms together

(r1-x)(r2-x)(r3-x)(r4-x) ... (rk-x)

anonymous · Answer

therefore f(x) = (r1-x)(r2-x)(r3-x)(r4-x) ... (rk-x)

the only caveat is that sometimes they hate to see a negative leading coefficient, to avoid that you would want to swap your x and root in the terms;  x - r

anonymous · Answer

You first  see a negative coefficient to avoid that you would want to swap your x and root in the terms; x-r