If a = 1, the sum α + β + γ + δ equals which of the following?

If a = 1, the sum α + β + γ + δ equals which of the following?

• A. -b
• B. b
• C. -d
• D. d

Answer: (A)

The sum of the roots of a polynomial is tied to its coefficients by Vieta’s formulas. For a quartic equation with leading coefficient a and coefficient b for the x^3 term, if the roots are α, β, γ, δ, then α + β + γ + δ = -b/a. Here a = 1, so α + β + γ + δ = -b. This matches the given option.

The sum of the roots of a polynomial is tied to its coefficients by Vieta’s formulas. For a quartic equation with leading coefficient a and coefficient b for the x^3 term, if the roots are α, β, γ, δ, then α + β + γ + δ = -b/a. Here a = 1, so α + β + γ + δ = -b. This matches the given option.