Question

How do you solve `15x ^ { 3} - 7x ^ { 2} - 2x = 0`?

Answer 1

0, .-2, `2/3`

Explanation:

First, we know that there are three zeroes in this equation (because of the variable in the leading coefficient is 3).

Since all the numbers in the polynomial has a "x" we can factor that out to get...

`x(15x^2-7x-2)`

Now, we know that if x=0, everything else will equal 0 (because the `x` on the outside will be 0 and it multiplies into everything else therefore making everything equal 0).

For the polynomial inside, we can use the quadratic equation (if you need to see all of the work or don't know what it is, ask me).

We should end up with:
`(7+13)/30` or `2/3` and `(7-13)/30` or `-0.2`.

Therefore the answers are `2/3, -0.2, and 0`.