Consider the polynomial x^3-3x-12. Show that this polynomial has a root between 1 and 2.

Question

aum · Answer

f(x) = x^3 - 3x - 12
f(1) = ?
f(2) = ?

If f(x) changes sign between x = 1 and x = 2, then it must pass through zero somewhere between 1 and 2.  So there will be a root between x = 1 and x = 2.

aum · Answer

Are you sure you typed the polynomial correctly?  Because the one you typed does not have a root between 1 and 2.

aum · Answer

It has a root between 2 and 3.

anonymous · Answer

Sorry! It's x^3+3x-12 @aum

aum · Answer

(x) = x^3 + 3x - 12 
f(1) = ? 
f(2) = ? 
If f(x) changes sign between x = 1 and x = 2, then it must pass through zero somewhere between 1 and 2. So there will be a root between x = 1 and x = 2 where f(x) = 0.