For the equation 3 x 2 + p x + 3 = 0 , p > 0 , if one of the roots is square of the other, then p is equal to

Step-by-step solution

Let α , α 2 be the roots of 3 x 2 + p x + 3 ∴ Product of the roots, α · α 2 = 1 ⇒ α 3 = 1 Again, α + α 2 = - p 3 ⇒   1 + 1 = - p 3 (if α = 1 ) ⇒   p = - 6 But p > 0 ∴   α = 1 is not possible. If α = ω , then α + α 2 = ω + ω 2 = - 1 ∴   - 1 = - p 3 ⇒ p = 3 Again, if α = ω 2 , then α + α 2 = ω 2 + ω 4 = ω 2 + ω = - 1 ∴   -