# Thread: Confusion in numerical methods

1. ## Confusion in numerical methods

Show that the positive root of the equation 1/x = x + 3 lies in the interval (0.30, 0.31).

From the sketch I found two intersection points. One in the +ve axis & another in the –ve axis. And I found sign change by substituting f(0.3) & f(0.31). But in the question says Show that the positive root of the equation, is it mean f(x) = 1/x – x - 3?

If there is a question about to show that the negative root of the equation, then what to do?

2. Originally Posted by geton
Show that the positive root of the equation 1/x = x + 3 lies in the interval (0.30, 0.31).

From the sketch I found two intersection points. One in the +ve axis & another in the –ve axis. And I found sign change by substituting f(0.3) & f(0.31). But in the question says Show that the positive root of the equation, is it mean f(x) = 1/x – x - 3?

If there is a question about to show that the negative root of the equation, then what to do?
To consider your question about the positive root, the intermediate value theorem says that if f(x) is continuous on [a, b] and f(a) < 0 and f(b) > 0, then there exists some c in [a, b] such that f(c) = 0. So let a = .30 and b = .31 and show that one of f(a), f(b) is positive and the other negative. Thus a root lies somewhere in that interval.

For the negative root you have no bounds set, so you'll have to do some work to find and a and b with the required properties.

-Dan