Let $\displaystyle \alpha ,\beta $ and $\displaystyle \gamma $ be the roots of the equation $( x-1) \displaystyle (x^{2}+x-3)=0.$ Then, the value of $\displaystyle (\alpha +\beta )$ is

Expanding the given equation (x - 1)(x^2 + x - 3) = 0 gives the standard cubic equation x^3 - 4x + 3 = 0. Let alpha, beta, and gamma be the roots of this cubic equation. The value alpha + beta can be found by subtracting the third root, gamma, from the sum of all roots, which is given by the formula -b/a. The sum of all three roots is 0, and from the factored form it is clear that x = 1 is a root, so we can set gamma = 1. Therefore, alpha + beta = 0 - 1 = -1.

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