2015/015) The roots of the cubic x^3-9x^2+mx-24=0 are in AP. Find m and the roots

The roots are in AP so they are , a-b, a, , a +b and b > 0

sum of roots = 3a = 9 hence a = 3

now product of roots = a(a-b)(a+b) = 24 or 3(3-b)(3+b) = 24 or $9-b^2 = 8$ and hence b = 1 

so roots are p = 2, q = 3, r = 4 

m = pq+ qr + rp = 26 = 2* 3 + 3 * 4 + 4 * 2 = 26 

hence roots are 2,3, 4 and m = 26