The third order polynomial y = x³ + (3 + √5) · x² - (18 - 6√5) · x has zeros in - 6, 0 and 3 - √5.
How to find a least degree polynomial
By the factor form of the polynomials, we know that the least degree contains a number of binomials equal to the number of roots and a leading coefficient. In this case, we have a polynomial of the following form:
y = 1 · (x + 6) · x · (x - 3 + √5)
y = x · (x + 6) · (x - 3 + √5)
y = x · [x² + (3 + √5) · x - 18 + 6√5]
y = x³ + (3 + √5) · x² - (18 - 6√5) · x
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