Let 2x5 5x4 x3 x2 x 6 0 be a polynomial equation Find

Let 2x^5 - 5x^4 + x^3 + x^2 - x + 6 = 0 be a polynomial equation. Find the list of all potential rational solution(s) for the polynomial equation using the Rational Root. Theorem then find the actual rational solution(s). Find all potential rational solution(s) Find all distinct actual rational solution(s).

Solution

A) Using the rational roots theorem, it is the factors of 6 (constant term) divided by the factors of 2 (coefficient of x^5).

So we have ±6, ±3, ±2,±1,±3/2,±1/2

B) The distinct actual rational solutions are ±i (these are complex solutions)