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# Major confusion with Linear interpolation Watch

1. ok, basically I'm given this question:

Use linear interpolation to find the positive root of the equation:
x^3 - 5x + 3 = 0, correct to one decimal place.

So I'm not given an interval to work with. Anyhow, I subbed in x = 0 and x = 1 into the equation to find that it changes sign between those two values, which therefore (as far as I'm aware) means this is where the root lies. So I used x = 0 and x= 1 as my starting interval.

However I ended up with a different answer to the one in the solutions page. (I got x = 0.6, whereas apparently it should be x = 1.8)

In the official solutions page, they used the interval x = 1 and x = 2. The answer of the equation also changes sign if those values are subbed in. So a root also lies there as well.

I'm confused at whether I'm wrong. Because there is a root in the interval which I used. But clearly this isn't what I'm supposed to have done - as shown by my incorrect answer and the different interval chosen in the solutions page, yet methodically and technically, I think I've done nothing wrong
2. (Original post by W.H.T)
ok, basically I'm given this question:

Use linear interpolation to find the positive root of the equation:
x^3 - 5x + 3 = 0, correct to one decimal place.

So I'm not given an interval to work with. Anyhow, I subbed in x = 0 and x = 1 into the equation to find that it changes sign between those two values, which therefore (as far as I'm aware) means this is where the root lies. So I used x = 0 and x= 1 as my starting interval.

However I ended up with a different answer to the one in the solutions page. (I got x = 0.6, whereas apparently it should be x = 1.8)

In the official solutions page, they used the interval x = 1 and x = 2. The answer of the equation also changes sign if those values are subbed in. So a root also lies there as well.

I'm confused at whether I'm wrong. Because there is a root in the interval which I used. But clearly this isn't what I'm supposed to have done - as shown by my incorrect answer and the different interval chosen in the solutions page, yet methodically and technically, I think I've done nothing wrong
Well there are two positive roots to this equation so it's wrong for the question to say the positive root.

Based on what you've posted I'd say you've done nothing wrong .

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Updated: December 29, 2010
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