Does anyone know a free app or site that I can use to solve the following equation:
$ 2a+4bx^2 -q c x^{q-2}=0 $, where, $a, b, c\in \mathbb{R}$, $a, b, c>0$ and $q>2$.
I would appreciate any help. Thanks in advance.
2026-03-27 00:57:02.1774573022
Finding zeros for $2a + 4bx^2 - qcx^{q-2} $
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If $q$ can be any number, the problem is purely numerical and you look for the positive zero of function $$f(x)=2a + 4bx^2 - qcx^{q-2}$$
I think that I should start simplifying using $4bx^2=t$ to make $$g(t)=2a+t-m t^n \quad \text{with}\quad m=c q(4b)^{1-\frac{q}{2}}>0\quad \text{and}\quad n=\frac q 2-1>0$$ This reduces the problem to the intersection of a straight line and an increasing power function.