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SymPy:

DiracDelta (x**2+x-2).simplify (x)

$\frac{\delta\left(x - 1\right)}{3} + \frac{\delta\left(x + 2\right)}{3}$

Plot:

Roots:

solve(DiracDelta(x - 1)/3 + DiracDelta(x + 2)/3, x)

$x =$

diff(DiracDelta(x - 1)/3 + DiracDelta(x + 2)/3, x)

$\frac{d}{d x} \left(\frac{\delta\left(x - 1\right)}{3} + \frac{\delta\left(x + 2\right)}{3}\right) =$

series(DiracDelta(x - 1)/3 + DiracDelta(x + 2)/3, x, 0, 10)

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