how many solutions has this equation:
$$ {x}^{3}+4\,{x}^{2}-1=0 $$
i tried ruffini so far and it is not working, now i'm stuck and no idea of how to aproach this.
[Math] How many solutions has this third degree equation
algebra-precalculuscalculuspolynomials
Best Answer
The derivative of $f(x)=x^3+4x^2-1$ is $f\,'(x)=3x^2+8x$, which is $0$ at $x=0$ and at $x=-\frac83$. Since the function is cubic with a positive leading coefficient, it has a local maximum at $x=-\frac83$ and a local minimum at $x=0$. If you calculate $f\left(-\frac83\right)$ and $f(0)$, you should be able to tell very quickly how many real solutions the equation has.