The correct option is A 14,12,34
Sum of the roots =−ba=−(−4832)=32
Check for the options.
Only option (a) gives sum equal to 32, hence is correct answer.
Alternatively:
Let the roots be a - d, a, a + d
Let us also compare the equation with ax3+bx2 + cx + d = 0
The sum of the roots =−ba=−(−4832)=32
⇒ a - d + a + a + d =32⇒a=12
Product of the roots =−(−332)
a(a2−d2)=332⇒ ((12)2−d2)=332×2⇒ d2=116⇒ d=±14
Roots are 12, (12+14), (12−14)=12, 34, 14