Question

Find the rational roots of the polynomial
x ⁴ −8x³+7x² −40x−60.

Answer 1

The rational roots of the polynomial x^4 - 8x^3 + 7x^2 - 40x - 60 can be found using the Rational Root Theorem.

Step-by-step explanation:

The rational roots of a polynomial can be found using the Rational Root Theorem. For the polynomial x^4 - 8x^3 + 7x^2 - 40x - 60, the constant term is -60 and the leading coefficient is 1. The possible rational roots are the factors of the constant term divided by the factors of the leading coefficient. In this case, the possible rational roots are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, and ±60. To determine which of these roots are actual roots of the polynomial, we can use synthetic division.