Given:
The equation of polynomial is
[tex]2x^3-5x^2+1=0[/tex]
To find:
All rational roots of the polynomial.
Solution:
According to the rational root theorem, all the possible rational roots of a polynomial are defined as
[tex]x=\dfrac{p}{q}[/tex]
where, p is a factor of constant term and q is factor of leading coefficient.
We have,
[tex]2x^3-5x^2+1=0[/tex]
Here, leading coefficient is 2 and constant term is 1.
Factors of 1 are ±1.
Factors of 2 are ±1, ±2.
Using rational root theorem, we get
[tex]x=\pm \dfrac{1}{1},\pm \dfrac{1}{2}[/tex]
[tex]x=\pm 1,\pm \dfrac{1}{2}[/tex]
Therefore, all possible rational roots of the given polynomial are [tex]\pm 1,\pm \dfrac{1}{2}[/tex].
