From looking at the coefficients of the cubic:
the sum of the roots equals 15;
the sum of the pairwise products of the roots equals 0;
and the product of the roots equals -Q.
Since the roots are in arithmetic progression, the roots can be expressed as a-d, a, a+d.
Then a-d + a + a+d = 15
and (a-d)*a + (a-d)*(a+d) + a*(a+d) = 0
and (a-d)*a*(a+d) = -Q
From the first equation we get a=5.
Then substituting this into the second equation yields (5-d)*5 + (5-d)*(5+d) + 5*(5+d) = 0
Simplifying gives 75 - d^2 = 0, or d^2=75.
The third equation simplifies into a*(d^2-a^2) = Q.
Then substituting a=5 and d^2=75 yields 5*(75-5^2) = 250 = Q.
Solution
