If α, β are the roots of the equation x² - 4x - 5 = 0 then α² + β² equals to:

Question: If α, β are the roots of the equation x² - 4x - 5 = 0 then α² + β² equals to:

Solution:
x² - 4x - 5 = 0
⇒ x² - 5x + x - 5 = 0
⇒ x(x - 5) + 1(x - 5) = 0
⇒ (x - 5)(x + 1) = 0
∴ x = 5, -1

Hence, α = 5 , β = -1 Hence, The value of α² + β² = 5² + (-1)² = 25 + 1 = 26