Question

List all the rational roots of f(x)= 24x^3-10x^2-7x+2

Answer 1

`x=-0.5,0.25,(2)/(3)`

Explanation:

`f(x)=24x^3+10x^2-7x+2`

For rational roots,
`f(x)=0`,so

`24x^3+10x^2-7x+2=0`

We can look at the factors for the constant term and the term multiplying the highest power to see if we can find candidates possible roots.

Factors of 2:

2, 1

Factors of 24:

24, 12, 6, 2, 4, 1, 2, 3, 8

We divide these factors of the constant term by the factors of the
`x^3` term to give us possible factors.

This gives us a set of:

`\pm \{(1)/(12),(1)/(24), (3)/(6), (1)/(6), 1, (1)/(2), (2)/(3), (1)/(3),(1)/(4),(1)/(8) \}`

We check all of these roots, by plugging them into the function to see if that will give us a result of 0.

We find the results that give us 0 are:

`x=-0.5,0.25,(2)/(3)`

Answer 2

A on EDGE

Explanation: