Find Zeros of f(x): Solving Functions Problem Homework

[luludatis]

Homework Statement

For the function f(x)=4x³-2x²-8x+2, the slope at any point on f(x) can be calculated using the equation m(x)=12x²-4x-8

Weirdly enough, I was able to answer all other 5 questions about this, except for the basics:

What are the zeroes of f(x)

Homework Equations

rational zeroes: +-p/q

The Attempt at a Solution

tried every possible rational zero. I just plugged it into the calculator and it gives me an answer, but I'm not sure if that is what we are supposed to do. I'm just trying to corroborate if there is not another way of solving it.

 

[gb7nash]

You could always use the cubic formula, but that's a beast.

 

[luludatis]

never used it, she did not teach it to us, so calculator it is :] thank you!

 

[gb7nash]

Do you know Newton's or bisection method?

 

[luludatis]

i don't think so...