How do you solve $xc^x + x + 1 = 0$ for $x$, where $c$ is a constant?
Solving $y = xc^x + x + 1$, where c is a constant
2
$\begingroup$
calculus
-
1Title $\ne$ body. Do you want $y$ in there, or do you want zero? Please decide and edit accordingly. – 2011-10-23
1 Answers
2
There doesn't exist a simple formula, in terms of elementary functions, for finding the roots of functions of this form.
If you need the root for particular $c$ (and $c\neq 0, 1$) you will need to approximate the root, for instance by plotting the function and looking for $x$-intercepts, or asking Wolfram Alpha. There also exist advanced numerical techniques, such as Newton's Method, that you could use to very accurately approximate roots of functions yourself.
-
0No. But if you're a precalculus student, using Alpha as a black box to plot and find the root is a reasonable approach to the problem, while understanding and implementing Newton's method is likely not (unless your precalc class was a lot more interesting than mine!) I've tried to clean up the wording of the answer. – 2011-10-23