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{ }(1,5)/(1,2) \\ \\ \pm(1)/(2),\text{ }\pm1,\text{ }\pm(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 = -}(1)/(2)`

Answer:

The possible rational roots are

`\begin{gathered} x\text{ = 1} \\ x\text{ = -}(1)/(2) \end{gathered}`