If the roots of p(x) = x^3 - 15x^2 + 74x + c form an arithmetic sequence, find c.
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,
\(\displaystyle a = 5,\\ d = 1, \\ c = -120.\)
