jmc

Question

Let r_1, r_2, and r_3 be the roots of x^3 - 3x^2 + 8 = 0.Find the monic polynomial, in x, whose roots are 2r_1, 2r_2, and 2r_3.

Accepted Answer

Let y = 2x. Then x = y2, so y^38 - 3y^24 + 8 = 0.Multiplying by 8, we get y^3 - 6y^2 + 64 = 0. The corresponding polynomial in x is then x^3 - 6x^2 + 64.