Show that f(x) = x^3 - 2x - 1 has a real zero between 1 and 2.

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Accepted Answer

Hi there. So this problem tells us to consider the following polynomial F of x equals X. The third minus five X plus one. And prove that there is a real zero between zero and one. So the proof that there's a real zero. I want to check to see if there's a sign change between our outputs because on the graph, if we go from negative to positive or positive negative, our line is most likely crossing the X axis. So let's go ahead and check our outputs. So let's say we use X equals zero as our first one. Let's put this into our equation. We have zero cubes minus five times zero plus what On the other side you can check our f. of one. So yeah F of one or X is equal to one. F of one equals one to the third minus five times one plus one. Let's simplify this. F zero is equal to zero cubed minus 10 plus one which is just one On the other side F of one. Once the third one is five times one plus one doesn't give us one minus five plus one. That doesn't give us negative three. So we notice here we have F0 as a positive value one. If one is a negative value -3. Since we are changing our son From F. O. Z. Articles 1 2. F 183. We have a sign change which means there could be a route between those two answers to those two outfits. Many of that I'm gonna say this is answer D. Because there is a sign change between those two outputs that indicates that there is a route between X and zero and X equals one. I have to help you solve the problem. Thank you for watching. Goodbye.

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