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

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In summary, the function f(x)=4x3-2x2-8x+2 has a slope that can be calculated using the equation m(x)=12x2-4x-8. The question of finding the zeroes of f(x) was discussed, with the suggestion of using the rational zeros theorem or the cubic formula. Other methods such as the Newton's or bisection method were also mentioned. However, the use of a calculator was deemed acceptable.
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luludatis
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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.
 
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  • #2
You could always use the cubic formula, but that's a beast.
 
  • #3
never used it, she did not teach it to us, so calculator it is :] thank you!
 
  • #4
Do you know Newton's or bisection method?
 
  • #5
i don't think so...
 

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

1.

What are the steps for finding the zeros of a function?

To find the zeros of a function, you can follow these steps:
1. Set the function equal to zero
2. Factor the function if possible
3. Use the Zero Product Property to find the values that make the function equal to zero
4. Check your answers by plugging them back into the original function.

2.

Why is it important to find the zeros of a function?

Finding the zeros of a function can help us understand the behavior of the function and its graph. It can also help us identify the x-intercepts, which are important points on a graph and can be used to solve real-world problems.

3.

What do the zeros of a function represent?

The zeros of a function represent the x-values where the function intersects the x-axis. In other words, they are the solutions to the equation f(x) = 0.

4.

Can all functions have zeros?

No, not all functions have zeros. For example, constant functions, such as f(x) = 5, do not have any zeros. Additionally, some functions may have complex or imaginary zeros, which are not real numbers.

5.

How do I know if my answer for the zeros of a function is correct?

You can check your answers by plugging them back into the original function. If the function equals zero when you substitute your answer for x, then it is a correct solution. You can also use a graphing calculator to visualize the function and its zeros.

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