The transformed equation is 8x3−54x−78=0 Root of cubic equation f(x)=0 are diminished by ‌
−3
2
Since, we don't have the original equation but the transformed equation. Therefore, we will verify it through the option. On taking option (a), we have ‌f(x)=2x3−9x2−6 ‌f(x)=2x3−9x2+0x−6
∴‌A0y3+A1y2+A2y+A3=0 ‌2y3+0y2+(‌
−27
2
)y−‌
39
2
=0 ⇒2y3−‌
27y
2
−‌
39
2
=0 ⇒8y3−54y−78=0 ⇒8x3−54x−78=0 which is the transformed equation.