Question

α, β are the roots of the equation $x^2$ + 4x + 5. Find ${\alpha }^3$ + ${\beta }^3$

• A. -4
• B. 4
• C. -6
• D. 6

Answer 1

The correct option is A

-4

α + β = -4

αβ = 5

${(\alpha +\beta )}^3$= ${\alpha }^3$ + ${\beta }^3$ + 3αβ(α + β)

⇒ ${\alpha }^3$ + ${\beta }^3$ = ${(\alpha +\beta )}^3$ - 3αβ(α + β)

= ${(-4)}^3$ - 3 × (5) × (-4)

= -64 + 60

= - 4