Respuesta :
Given:
The function is:
[tex]f(x)=10x^5+8x^4-15x^3+2x^2-2[/tex]
To find:
All the possible rational zeros for the given function by using the Rational Zero Theorem.
Solution:
According to the rational root theorem, all the rational roots are of the form [tex]\dfrac{p}{q},q\neq 0[/tex], where p is a factor of constant term and q is a factor of leading coefficient.
We have,
[tex]f(x)=10x^5+8x^4-15x^3+2x^2-2[/tex]
Here,
Constant term = -2
Leading coefficient = 10
Factors of -2 are ±1, ±2.
Factors of 10 are ±1, ±2, ±5, ±10.
Using the rational root theorem, all the possible rational roots are:
[tex]x=\pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}[/tex].
Therefore, all the possible rational roots of the given function are [tex]\pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}[/tex].
