Cuby :>)

Let the roots of the equation be $\alpha,\beta,\gamma$ .

From vieta's formula ,

$\alpha+\beta+\gamma=-a$

$\alpha\beta+\beta\gamma+\gamma\alpha=b$

$\alpha\beta\gamma=-(-1)=1$

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From AM - GM inequality , for non-negative real roots,

$\dfrac{\alpha+\beta+\gamma+\alpha\beta+\beta\gamma+\gamma\alpha}{6}\ge\sqrt[6]{\alpha\cdot\beta\cdot\gamma\cdot\alpha\beta\cdot\beta\gamma\cdot\gamma\alpha}$

$\dfrac{b-a}{6}\ge\sqrt[6]{(\alpha\beta\gamma)^3}$

$\dfrac{b-a}{6}\ge\sqrt[6]{1^3}$

$\boxed{b-a\ge 6}$

Therefore, the minimum value of b-a is 6