Posted by **Anonymous** on Thursday, October 18, 2012 at 11:34am.

Show that the equation x^5+x+1 = 0 has exactly one real root. Name the theorems you use to prove it.

I.V.T.

*f(x) is continuous

*Lim x-> inf x^5+x+1 = inf >0

*Lim x-> -inf x^5+x+1 = -inf <0

Rolles

*f(c)=f(d)=0

*f(x) is coninuous

*f(x) is differentiable

f'(x) = 5x^4+1=0

As f'(x) does not equal zero, because of rolles theorem, the assumptioin f(x) has two roots is false.

Used Intermediate Value theorem and Rolles Theorm.

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