# Intermediate Value Theorem to show that there is a root in a given equation/interval

• Sep 20th 2009, 11:26 AM
s3a
Intermediate Value Theorem to show that there is a root in a given equation/interval
Question: Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.

37.

x^4 + x - 3 = 0, (1,2)

What do I do for this question? Do I plug in 1 and 2 and try to estimate something in the middle, like I don't get what it is asking in the first place. Like what does "a root of the given equation in the specified interval" mean?

Any help would be greatly appreciated!
• Sep 20th 2009, 11:28 AM
Arturo_026
Yes, plug your x values and according to IVT if one is possitive and the other is negative, than there has to be a root between thos numbers...ofcourse since the function is a polynomial therefore it's continuous.
• Sep 20th 2009, 11:35 AM
s3a
So the question is not asking me to show "the root of the given equation," right? But what does that mean exactly?
• Sep 20th 2009, 11:37 AM
Arturo_026
Quote:

Originally Posted by s3a
So the question is not asking me to show "the root of the given equation," right? But what does that mean exactly?

A root is also know as a zero, or where the graph crosses the x-axis.
So u just have to substitute x for your given values and checkk their signs.