If - 2 and 3 are roots of the equation a₀+a₁ x+a₂ x^2+a₃ x^3+x^4=0 where a₀, a₁, a₂, a₃ are integers, then which one of the following is correct?

Step-by-step solution

- 2 and 3 are roots of the given equation Therefore 2 and - 3 are also roots of the given aligned & equation x^4+a₃ x^3+a₂ x^2+a₁ x+a₀ & =(x+ 2 )(x- 2 )(x- 3 )(x+ 3 ) & = (x^2-2 ) (x^2-3 ) & =x^4-3 x^2-2 x^2+6 & =x^4-5 x^2+6 & a₃=0, a₂=-5, a₁=0 and a₀=6 . aligned