Please excuse me if the question seems to commonplace. Can Mathematica give a response to this question:
In which condition related to the coefficients c>0, \, n\geq 2, 0<p<1,\, a>c, \, \, \text{and} \, \, b>0, this equation
F(x)= -c x^{n+p} -bx^n + (a-c)x^p -b \qquad (*)
have solution in \mathbb R.
Assumptions:
assum = And @@ {c > 0, n >= 2, 0 < p < 1, a > c, b > 0}
Function:
f[x_] := -c x^(n + p) - b x^n + (a - c) x^p - b
And I find this way to do it
assum = And @@ {c > 0, n >= 2, 0 < p < 1, a > c, b > 0}
f[x_] := -c x^(n + p) - b x^n + (a - c) x^p - b
Assuming[assum, FullSimplify@Reduce[f[x] == 0, Reals]]
