Posted by **cel** on Monday, November 29, 2010 at 9:31pm.

Show that the equation x^3 - 15x + c = o has exactly one real root.

All I know is that it has something to do with the Mean Value Theorem/Rolle's Theorem.

- AP Calculus -
**Reiny**, Monday, November 29, 2010 at 11:25pm
You must have a typo.

There are all kinds of values of c for which the above equation has 3 roots.

e.g. if c=0

x^3 - 15x = 0

x(x^2 - 15) = 0

x = 0 or x = ± √15

are you sure it wasn't x^3 + 15x + c = 0 ?

I will assume it was

It's been 50 years but if I recall, Rolle's theorem says that if there are two x-intercepts , then the derivative must be zero between those two points

so let f(x) = x^3 + 15x + c

f '(x) = 3x^2 +15 = 0

notice this is always positive, since x^2 = -5 has no real solution,

so there are no turning points, and the curve cuts only once.

You do know that every cubic must cut he x-axis at least once?

- AP Calculus -
**Alon**, Thursday, December 8, 2011 at 2:21am
The missing info it the interval [-2,2]. In this interval there could be just one root.

## Answer This Question

## Related Questions

- Math - Calculus - Show that the equation x^3-15x+c=0 has at most one root in the...
- Math - Calculus - Show that the equation x^3-15x+c=0 has at most one root in the...
- Calculus - Let f(x)=3x^5+5x^3+15x+15. Use Rolle's Theorem to show that f(x) has ...
- CALCULUS! - suppose that 3 <_ f prime of x <_ 5, for all values x. show ...
- calculus - Show that the function f(x)=4x^3−15x^2+9x+8 satisfies the ...
- calc - Verify that the function satisfies the three hypotheses of Rolle's ...
- calculus - Referring to the Mean Value Theorem and Rolle's Theorem, how can I ...
- calc - Verify that the function satisfies the three hypotheses of Rolle's ...
- Calculus (Please Check) - Show that the equation x^5+x+1 = 0 has exactly one ...
- Math - Let f(x) = 2x + 1 − sin(x), how many roots does f(x) have in the ...

More Related Questions