Question

for each of the following find all rational roots of the polynomial equation​ ​ 2x cube - 5 x square + 1=0 ​​

Answer 1

Given:

The equation of polynomial is

`2x^3-5x^2+1=0`

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

`x=(p)/(q)`

where, p is a factor of constant term and q is factor of leading coefficient.

We have,

`2x^3-5x^2+1=0`

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

`x=\pm (1)/(1),\pm (1)/(2)`

`x=\pm 1,\pm (1)/(2)`

Therefore, all possible rational roots of the given polynomial are
`\pm 1,\pm (1)/(2)`.