In the quadratic z^2 - (α+β) z + αβ = 0, what is the sum of the roots?

In the quadratic z^2 - (α+β) z + αβ = 0, what is the sum of the roots?

• A. α
• B. αβ
• C. α + β
• D. -(α+β)

Answer: (C)

For a quadratic, the sum of the roots equals the negative of the coefficient of z. Here the coefficient of z is -(α+β), so the sum of the roots is - [-(α+β)] = α+β. You can also factor the quadratic as (z - α)(z - β) = z^2 - (α+β)z + αβ, whose roots are α and β, whose sum is α+β.

For a quadratic, the sum of the roots equals the negative of the coefficient of z. Here the coefficient of z is -(α+β), so the sum of the roots is - [-(α+β)] = α+β. You can also factor the quadratic as (z - α)(z - β) = z^2 - (α+β)z + αβ, whose roots are α and β, whose sum is α+β.