If a differentiable function $f\left(x\right)$ has a relative minimum at $x=0,$ then the function $y=f\left(x\right)+ax+b$ has a relative minimum at $x=0$ for

Let $f\left(x\right)=a{x}^3+5x^2+cx+1$ be a polynomial function. If $f\left(x\right)$ has extreme at $x=\alpha$ and $\beta$ such that $\alpha \beta <0$ and $f\left(\alpha \right)f\left(\beta \right)<0$, then the equation $f\left(x\right)=0$ has