If alpha and beta are the roots of the equation 2x^2+ 4x + 1 = , find the values of log2alpha + log2beta

Answer 1

If 2x²+4x+1 = 0
Then: x = (-2±√2)/2

let α = (-2+√2)/2
let β = (-2-√2)/2

log_2(α) + log_2(β)
= log_2(αβ)
= log_2((-2+√2)(-2-√2)/4)
= log_2(1/2)
= -1