Question

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

Answer 1

Answer:

$x=-0.5,0.25,\frac{2}{3}$

Step-by-step 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:

$\pm \{\frac{1}{12},\frac{1}{24}, \frac{3}{6}, \frac{1}{6}, 1, \frac{1}{2}, \frac{2}{3}, \frac{1}{3},\frac{1}{4},\frac{1}{8} \}$

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:

$x=-0.5,0.25,\frac{2}{3}$

Answer 2

Answer:

A on EDGE

Step-by-step explanation: