Question

List the possible rational roots of the equation & solve:2x^4 -9x^3 + 13x^2 - x -5 =0

Answer 1

Given:

$2x^4\:-\:9x^3\:+\:13x^2\:-x-5\:=\:0$

Using the rational root theorem

The rational root theorem, also called rational root test, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.

The following rational roots are possible:

$\begin{gathered} \pm\text{ }\frac{1,5}{1,2} \\ \\ \pm\frac{1}{2},\text{ }\pm1,\text{ }\pm\frac{5}{2},\text{ }\pm5 \end{gathered}$

Next, we validate the roots by plugging them into the polynomial

The only roots that satisfy the polynomial includes :

$x\text{ = 1, x = -}\frac{1}{2}$

Answer:

The possible rational roots are

$\begin{gathered} x\text{ = 1} \\ x\text{ = -}\frac{1}{2} \end{gathered}$