Polynomial coefficients of $f(x) = \frac{1}{100} e^{5x} - \frac{1}{4}$

Question

Can anybody tell me what the polynomial coefficients are for this function?

$f(x) = \frac{1}{100} e^{5x} - \frac{1}{4}$

I'm just trying to get the function coefficient vector and then use "roots" function in Scilab to get polynomial root.

When I have simple fuction like this: $$f(x) = x^2 + x - 1$$ then I know that my function coefficient vector is: $[1,1,-1]$.

Answer 1

If you are just trying fo find a solution to a general non-linear equation, then you can use fsolve:

function y=f(x)
    y=exp(5*x)/100 -1/4
end

x=fsolve(1,f)

--> disp(x)

   0.6437752

Answer 2

The exponential function $e^x$ is trascendental (not algebraic, i.e., not expressible exactly as a polynomial, a ratio of polynomials, or roots of the above). So are the logarithm and trigonometric functions (elementary trascendental functions). You can't get the coefficients as a polynomial for your function, as it is not a polynomial.

Answer 3

It's not a polynomial, so we can't speak of polynomial coefficient

Are you interested in its Taylor series

$\frac{-6}{25}+\frac{x}{20}+\frac{x^2}{8}+\frac{5*x^3}{24}+\frac{25*x^4}{96}+\frac{25*x^5}{96}+\frac{125*x^6}{576}+..........$