jmc

Question

Let r_1, r_2, r_3, and r_4 be the roots of x^4 - 2x^3 - 5x^2 + 4x - 1 = 0.Find the monic polynomial, in x, whose roots are 1r_1, 1r_2, 1r_3, and 1r_4.

Accepted Answer

Let x = 1y, so 1y^4 - 2y^3 - 5y^2 + 4y - 1 = 0.To turn this into a monic polynomial, we multiply by -y^4, which gives us y^4 - 4y^3 + 5y^2 + 2y - 1 = 0. The corresponding polynomial in x is then x^4 - 4x^3 + 5x^2 + 2x - 1 = 0.