Homework Help: Calculus (Please Check)

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.

Calculus (Please Check) - Damon, Thursday, October 18, 2012 at 12:10pm
you mean f'(x) has no real roots I think.
It does cross the x axis at least once as you showed with intermediate value
however the slope is never zero so it never can cross the axis again. The other four roots are therefore complex numbers.

Answer this Question

Related Questions

AP Calculus - Show that the equation x^3 - 15x + c = o has exactly one real root...
math - 4.2 18. show that the equation 2x-1-sinx=0 has exactly one real root.
Algebra - For what value(s) of b will x^2 + bx + 3 have exactly one root? I'...
math - I HAVE THESE ANSWERS FOR THE PROBLEMS. COULD YOU DOUBLE CHECK PLEASE, ...
math - Could you please solve so I can double check my answers for the practice ...
Calculus - Let f(x)=3x^5+5x^3+15x+15. Use Rolle's Theorem to show that f(x) ...
Precalculus - For our homework we had to read this one section which ...
Math - For what value of k does the equation x2 + k = kx – 8 have: Two ...
math - show that the equation 2x-1-sinx=0 has exactly one real root. sin x = 2x-...
college algebra - 1. solve the following logarithmic equation log_8(x+8)+log_8(x...

For Further Reading

First Name:
School Subject:
Answer: