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Algebra/Zeros of the function

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Expert: - 8/29/2009


Question
In this problem i have to solve it algebraically and i do not know how to approach it.Can you please give me the first two steps to solving this: F(x)=1/2x^3-x

Answer
Hello Kendria,

As you probably know, the zeroes are the solutions of the equation.

F(x) = 0             ...(1)

In your case that would be

0.5x^3-x = 0          ...(2)  

By "solutions" I mean the values for "x" that satisfy the equation, those are the zeroes. So how do you
find them? Well what you should always try first is to factor the left hand side of equation (2). There is
at least one "x" on both terms so we can write it as:

(0.5x^2 - 1)x = 0

Now let's take a moment to see what we have here. We have a product of terms that gives us zero, right?
That means that, at least one of the factors MUST be zero.

So either

(0.5x^2 - 1) = 0

or

x=0

...I'll stop there because it's my policy not to give full answers to problems like this. But hopefully this will help you get started.

Hope this is clear, please let me know if it isn't.

Cheers,
David

Algebra

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