As the degree of given polynomial is ‘3’, hence it will have three zeroes Let α β γ be the zeroes of the given polynomial Now α β γ are in A.P. ∴ Let α=a−dβ=a and γ=a+d Now α+β+γ=
144
64
∴ 3a=
144
64
∴ a=
144
64×3
=
3
4
and αβγ=
15
64
∴ (a−d)(a)(a+d)=
15
64
∴ a(a2−d2)=
15
64
∴
3
4
(
9
16
−d2)=
15
64
∴
9
16
−d2=
5
16
∴ d2=
9
16
−
5
16
=
4
16
∴ d2=
1
4
∴ d=±
1
2
Now difference between largest and smallest zeroes of polynomial =(a+d)−(a−d) =2d=2(
1
2
) (∴ In option all the values are +ve) =1 ∴ Option (a) is correct