If the roots of 10x3 - nx2 - 54x - 27 = 0 are in harmonic progression, then n equals ___________.

10x3−nx2−54x−27=0 has roots in H.P.put x = 1/t27t3+54t2+nt−10=0This equation has roots in A.P. Let the roots be a - d, a, and a + d∴ 3a=−5427 or a=−23Also (a−d)a(a+d)=1027∴     2349−d2=−1027 or 49−d2=−59∴     d2=1 or d=±1So, roots are 13,−23,−53∴ n27=109−59−29 or n27=39or n = 9