Polynomials

Suppose that the roots are

$\displaystyle a-d, a, a+d,$

then the equation will be

$\displaystyle (x-a+d)(x-a)(x-a-d) \\ =x^{3}-3ax^{2}+(3a^{2}-d)x-a^{3}+ad^{2} =0,$

so equating coefficients,

$\displaystyle a = 5,\\ d = 1, \\ c = -120.$