Find a lowest-degree polynomial

Question

Find a lowest-degree polynomial with real coefficients and leading coefficient 1, having zeros 1/2,-1, and 2/3.

Answer 1

For the zeros 1/2, -1, and 2/3 the factors of the polynomial are

 

(x - 1/2)(x + 1)(x - 2/3)

(x² - 7x/6 + 1/3)(x + 1)

x³ - x²/6 - 5x/6 + 1/3