Answer:
α² + β² = 5
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a≠ 0 ) , then
sum of roots = - [tex]\frac{b}{a}[/tex]
product of roots = [tex]\frac{c}{a}[/tex]
x² - x - 2 = 0 ← is in standard form
with a = 1, b = - 1, c = - 2 , then
α + β = - [tex]\frac{-1}{1}[/tex] = 1
αβ = [tex]\frac{-2}{1}[/tex] = - 2
Using the identity
(α + β)² = α² + β² + 2αβ , then
α² + β² = (α + β)² - 2αβ = 1² - 2(- 2) = 1 + 4 = 5
[tex] \large \boxed{ \boxed{\mathrm{ \alpha }^{2} + { \beta }^{2} = 5}}[/tex]
let's solve for :
let's plug the values,
[tex] \mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}[/tex]
