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Let α and β be the roots of the equation x^2 + x + 1 = 0. Then for γ ≠ 0 in R, | y+1 α β | | α y+β 1 | is equal to : | β 1 y+α |

1. y(y^2 - 3)
2. y^3
3. y(y^2 - 1)
4. y^3 - 1

Correct answer: y^3

Solution

The determinant of the matrix formed by the roots α and β, along with the variable y, simplifies to y^3 due to the properties of determinants and the specific values of α and β derived from the roots of the given quadratic equation.

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